Number Sets - SAT Math
Card 0 of 24
Which pair of number sets have no intersection?
Which pair of number sets have no intersection?
An intersection of two sets is defined as the set of elements that are members of both sets. The correct answer is the pair of sets that has no overlap.
Rationals are defined 
if a and b are integers. The irrationals are defined as any real number that is not rational. By definition a number cannot be both rational and irrational.
Prime numbers are divisible only by 1 and themselves. Even numbers are defined as integer multiples of 
. A number common to both sets is 
.
Natural numbers are the counting numbers, while the integers are all the naturals and their opposites. There are many elements common to both sets, such as 
:
The negatives are all the integers less than zero. And remember that an even number is defined as any integer multiple of two. Again there are many elements in common including 
:
The naturals are the counting numbers, while the wholes are all the naturals and zero. These two sets share many elements in common such as 
.
An intersection of two sets is defined as the set of elements that are members of both sets. The correct answer is the pair of sets that has no overlap.
Rationals are defined
Prime numbers are divisible only by 1 and themselves. Even numbers are defined as integer multiples of
Natural numbers are the counting numbers, while the integers are all the naturals and their opposites. There are many elements common to both sets, such as
The negatives are all the integers less than zero. And remember that an even number is defined as any integer multiple of two. Again there are many elements in common including
The naturals are the counting numbers, while the wholes are all the naturals and zero. These two sets share many elements in common such as
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set 
is the set of all positive integers.
Let 
be the set of all multiples of 2; let 
be the set of all multiples of 3; let 
be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
,
450 is a multiple of 3.
Therefore,
.
We are looking for an element of 
- that is, a multiple of 2, 3, and 5. All five choices are multiples of 5 (ending in a "5" or a "0"); 725 and 735 can be eliminated as they are not multiples of 2 (ending in a "5"). We test 720, 730, and 740 to find the multiple of 3:
720 is the correct choice.
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
450 is a multiple of 3.
Therefore,
We are looking for an element of
720 is the correct choice.
Compare your answer with the correct one above
Which of the above numbers does not fit with the rest of the set?
Which of the above numbers does not fit with the rest of the set?
In the above set, four of the numbers are all even 
.
The only one that is not even, also making it your answer, is 
since it is an odd number.
In the above set, four of the numbers are all even
The only one that is not even, also making it your answer, is
Compare your answer with the correct one above
Which of the following sets is closed under multiplication?
Which of the following sets is closed under multiplication?
A set is closed under multiplication if and only if the product of any two (not necessarily distinct) elements of that set is itself an element of that set.
This can easily be disproved in the case of three of these sets:
But closure can be proved to hold in the case of 
. Each number takes the form of 
for some nonnegative integer 
. If we multiply two numbers in this form, we get
which is an element of 
, being of this form.
A set is closed under multiplication if and only if the product of any two (not necessarily distinct) elements of that set is itself an element of that set.
This can easily be disproved in the case of three of these sets:
But closure can be proved to hold in the case of
which is an element of
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set is the set of all positive integers.
Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?
From the last digit, it can be immediately determined that 873 is not a multple of 2 or 5; since 
, 873 is a multiple of 3. Therefore,
We are looking for an integer that is also in this set - that is, one that is also a multiple of 3 but not 2 or 5. From the last digits, we can immediately eliminate 366 and 368 as multiples of 2 and 365 as a multiple of 5. We test 367 and 369 to see which one is a multiple of 3:
369 is the correct choice.
From the last digit, it can be immediately determined that 873 is not a multple of 2 or 5; since
We are looking for an integer that is also in this set - that is, one that is also a multiple of 3 but not 2 or 5. From the last digits, we can immediately eliminate 366 and 368 as multiples of 2 and 365 as a multiple of 5. We test 367 and 369 to see which one is a multiple of 3:
369 is the correct choice.
Compare your answer with the correct one above
What is the power set for the data set?
What is the power set for the data set?
The power set is the set of all subsets that can be created from the original set.
For the set 
, you can create the subsets:
This means that the power set is the set of all sets, so the power set is:
The power set is the set of all subsets that can be created from the original set.
For the set
This means that the power set is the set of all sets, so the power set is:
Compare your answer with the correct one above
Which pair of number sets have no intersection?
Which pair of number sets have no intersection?
An intersection of two sets is defined as the set of elements that are members of both sets. The correct answer is the pair of sets that has no overlap.
Rationals are defined if a and b are integers. The irrationals are defined as any real number that is not rational. By definition a number cannot be both rational and irrational.
Prime numbers are divisible only by 1 and themselves. Even numbers are defined as integer multiples of . A number common to both sets is .
Natural numbers are the counting numbers, while the integers are all the naturals and their opposites. There are many elements common to both sets, such as :
The negatives are all the integers less than zero. And remember that an even number is defined as any integer multiple of two. Again there are many elements in common including :
The naturals are the counting numbers, while the wholes are all the naturals and zero. These two sets share many elements in common such as .
An intersection of two sets is defined as the set of elements that are members of both sets. The correct answer is the pair of sets that has no overlap.
Rationals are defined
Prime numbers are divisible only by 1 and themselves. Even numbers are defined as integer multiples of
Natural numbers are the counting numbers, while the integers are all the naturals and their opposites. There are many elements common to both sets, such as
The negatives are all the integers less than zero. And remember that an even number is defined as any integer multiple of two. Again there are many elements in common including
The naturals are the counting numbers, while the wholes are all the naturals and zero. These two sets share many elements in common such as
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set is the set of all positive integers.
Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
,
450 is a multiple of 3.
Therefore,
.
We are looking for an element of - that is, a multiple of 2, 3, and 5. All five choices are multiples of 5 (ending in a "5" or a "0"); 725 and 735 can be eliminated as they are not multiples of 2 (ending in a "5"). We test 720, 730, and 740 to find the multiple of 3:
720 is the correct choice.
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
450 is a multiple of 3.
Therefore,
We are looking for an element of
720 is the correct choice.
Compare your answer with the correct one above
Which of the above numbers does not fit with the rest of the set?
Which of the above numbers does not fit with the rest of the set?
In the above set, four of the numbers are all even .
The only one that is not even, also making it your answer, is since it is an odd number.
In the above set, four of the numbers are all even
The only one that is not even, also making it your answer, is
Compare your answer with the correct one above
Which of the following sets is closed under multiplication?
Which of the following sets is closed under multiplication?
A set is closed under multiplication if and only if the product of any two (not necessarily distinct) elements of that set is itself an element of that set.
This can easily be disproved in the case of three of these sets:
But closure can be proved to hold in the case of . Each number takes the form of for some nonnegative integer . If we multiply two numbers in this form, we get
which is an element of , being of this form.
A set is closed under multiplication if and only if the product of any two (not necessarily distinct) elements of that set is itself an element of that set.
This can easily be disproved in the case of three of these sets:
But closure can be proved to hold in the case of
which is an element of
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set is the set of all positive integers.
Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?
From the last digit, it can be immediately determined that 873 is not a multple of 2 or 5; since , 873 is a multiple of 3. Therefore,
We are looking for an integer that is also in this set - that is, one that is also a multiple of 3 but not 2 or 5. From the last digits, we can immediately eliminate 366 and 368 as multiples of 2 and 365 as a multiple of 5. We test 367 and 369 to see which one is a multiple of 3:
369 is the correct choice.
From the last digit, it can be immediately determined that 873 is not a multple of 2 or 5; since
We are looking for an integer that is also in this set - that is, one that is also a multiple of 3 but not 2 or 5. From the last digits, we can immediately eliminate 366 and 368 as multiples of 2 and 365 as a multiple of 5. We test 367 and 369 to see which one is a multiple of 3:
369 is the correct choice.
Compare your answer with the correct one above
What is the power set for the data set?
What is the power set for the data set?
The power set is the set of all subsets that can be created from the original set.
For the set , you can create the subsets:
This means that the power set is the set of all sets, so the power set is:
The power set is the set of all subsets that can be created from the original set.
For the set
This means that the power set is the set of all sets, so the power set is:
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set is the set of all positive integers.
Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
,
450 is a multiple of 3.
Therefore,
.
We are looking for an element of - that is, a multiple of 2, 3, and 5. All five choices are multiples of 5 (ending in a "5" or a "0"); 725 and 735 can be eliminated as they are not multiples of 2 (ending in a "5"). We test 720, 730, and 740 to find the multiple of 3:
720 is the correct choice.
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
450 is a multiple of 3.
Therefore,
We are looking for an element of
720 is the correct choice.
Compare your answer with the correct one above
Which of the above numbers does not fit with the rest of the set?
Which of the above numbers does not fit with the rest of the set?
In the above set, four of the numbers are all even .
The only one that is not even, also making it your answer, is since it is an odd number.
In the above set, four of the numbers are all even
The only one that is not even, also making it your answer, is
Compare your answer with the correct one above
Which pair of number sets have no intersection?
Which pair of number sets have no intersection?
An intersection of two sets is defined as the set of elements that are members of both sets. The correct answer is the pair of sets that has no overlap.
Rationals are defined if a and b are integers. The irrationals are defined as any real number that is not rational. By definition a number cannot be both rational and irrational.
Prime numbers are divisible only by 1 and themselves. Even numbers are defined as integer multiples of . A number common to both sets is .
Natural numbers are the counting numbers, while the integers are all the naturals and their opposites. There are many elements common to both sets, such as :
The negatives are all the integers less than zero. And remember that an even number is defined as any integer multiple of two. Again there are many elements in common including :
The naturals are the counting numbers, while the wholes are all the naturals and zero. These two sets share many elements in common such as .
An intersection of two sets is defined as the set of elements that are members of both sets. The correct answer is the pair of sets that has no overlap.
Rationals are defined
Prime numbers are divisible only by 1 and themselves. Even numbers are defined as integer multiples of
Natural numbers are the counting numbers, while the integers are all the naturals and their opposites. There are many elements common to both sets, such as
The negatives are all the integers less than zero. And remember that an even number is defined as any integer multiple of two. Again there are many elements in common including
The naturals are the counting numbers, while the wholes are all the naturals and zero. These two sets share many elements in common such as
Compare your answer with the correct one above
Which of the following sets is closed under multiplication?
Which of the following sets is closed under multiplication?
A set is closed under multiplication if and only if the product of any two (not necessarily distinct) elements of that set is itself an element of that set.
This can easily be disproved in the case of three of these sets:
But closure can be proved to hold in the case of . Each number takes the form of for some nonnegative integer . If we multiply two numbers in this form, we get
which is an element of , being of this form.
A set is closed under multiplication if and only if the product of any two (not necessarily distinct) elements of that set is itself an element of that set.
This can easily be disproved in the case of three of these sets:
But closure can be proved to hold in the case of
which is an element of
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set is the set of all positive integers.
Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?
From the last digit, it can be immediately determined that 873 is not a multple of 2 or 5; since , 873 is a multiple of 3. Therefore,
We are looking for an integer that is also in this set - that is, one that is also a multiple of 3 but not 2 or 5. From the last digits, we can immediately eliminate 366 and 368 as multiples of 2 and 365 as a multiple of 5. We test 367 and 369 to see which one is a multiple of 3:
369 is the correct choice.
From the last digit, it can be immediately determined that 873 is not a multple of 2 or 5; since
We are looking for an integer that is also in this set - that is, one that is also a multiple of 3 but not 2 or 5. From the last digits, we can immediately eliminate 366 and 368 as multiples of 2 and 365 as a multiple of 5. We test 367 and 369 to see which one is a multiple of 3:
369 is the correct choice.
Compare your answer with the correct one above
What is the power set for the data set?
What is the power set for the data set?
The power set is the set of all subsets that can be created from the original set.
For the set , you can create the subsets:
This means that the power set is the set of all sets, so the power set is:
The power set is the set of all subsets that can be created from the original set.
For the set
This means that the power set is the set of all sets, so the power set is:
Compare your answer with the correct one above
The above represents a Venn diagram. The universal set is the set of all positive integers.
Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
The above represents a Venn diagram. The universal set
Let
As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 450?
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
,
450 is a multiple of 3.
Therefore,
.
We are looking for an element of - that is, a multiple of 2, 3, and 5. All five choices are multiples of 5 (ending in a "5" or a "0"); 725 and 735 can be eliminated as they are not multiples of 2 (ending in a "5"). We test 720, 730, and 740 to find the multiple of 3:
720 is the correct choice.
450 ends in a "0" and is therefore a multiple of both 2 and 5. Also, since
450 is a multiple of 3.
Therefore,
We are looking for an element of
720 is the correct choice.
Compare your answer with the correct one above
Which of the above numbers does not fit with the rest of the set?
Which of the above numbers does not fit with the rest of the set?
In the above set, four of the numbers are all even .
The only one that is not even, also making it your answer, is since it is an odd number.
In the above set, four of the numbers are all even
The only one that is not even, also making it your answer, is
Compare your answer with the correct one above