Functions, Relations, & Cardinality - Introduction to Proofs

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Question

If

$\A= \left\{4, 12, 20, 25, 28\right\} \B= \left\{\varnothing, 4, 8, 19, 22, 28\right\} \C= \left\{\varnothing, 3, 4, 8, 13, 14\right\}$

Find the cardinality of $B\cap B$

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Answer

The question is asking us to find the number of elements in the intersection of B and B .

We simply find the common elements of the two sets, and count the number of elements.

$B\cap B = \left\{\varnothing, 4, 8, 19, 22, 28\right\}$
Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{6, 7, 10, 11, 19, 24\right\} \B= \left\{5, 8, 15, 17, 19, 28\right\} \C= \left\{1, 2, 3, 7, 9, 14\right\}$

Find the cardinality of $A\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and B .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap B = \left\{19\right\}$
Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{3, 4, 9, 10, 11, 16\right\} \B= \left\{2, 7, 10, 15, 16\right\} \C= \left\{\varnothing, 8, 14, 17, 18\right\}$

Find the cardinality of $A\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of A and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$A\cup A = \left\{3, 4, 9, 10, 11, 16\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{3, 8, 10, 21, 27, 29\right\} \B= \left\{5, 10, 11, 18, 21\right\} \C= \left\{\varnothing, 1, 2, 7, 9\right\}$

Find the cardinality of $B\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of B and B .

We simply find the common elements of the two sets, and count the number of elements.

$B\cap B = \left\{5, 10, 11, 18, 21\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{5, 10, 12, 13, 18, 21\right\} \B= \left\{\varnothing, 3, 4, 7, 10, 16\right\} \C= \left\{2, 4, 5, 7, 13\right\}$

Find the cardinality of $A\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and B .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap B = \left\{10\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{11, 12, 13, 14, 18\right\} \B= \left\{1, 10, 11, 14, 16\right\} \C= \left\{3, 6, 8, 10, 17\right\}$

Find the cardinality of $B\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of B and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$B\cup A = \left\{1, 10, 11, 12, 13, 14, 16, 18\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{9, 10, 16, 17, 19\right\} \B= \left\{3, 6, 8, 18\right\} \C= \left\{1, 7, 8, 10\right\}$

Find the cardinality of $A\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of A and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$A\cup A = \left\{9, 10, 16, 17, 19\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{1, 2, 4, 6, 11, 21\right\} \B= \left\{3, 10, 13, 14, 21, 22\right\} \C= \left\{2, 4, 5, 8, 12, 14\right\}$

Find the cardinality of $A\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and B .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap B = \left\{21\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{12, 22, 26, 28, 29\right\} \B= \left\{1, 4, 14, 15, 22, 24\right\} \C= \left\{\varnothing, 2, 4, 8, 13, 14\right\}$

Find the cardinality of $A\cap A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and A .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap A = \left\{12, 22, 26, 28, 29\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{\varnothing, 3, 11, 13, 16, 19\right\} \B= \left\{\varnothing, 3, 4, 11, 16\right\} \C= \left\{\varnothing, 2, 12, 19\right\}$

Find the cardinality of $A\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of A and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$A\cup A = \left\{\varnothing, 3, 11, 13, 16, 19\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{6, 8, 9, 11, 12, 13\right\} \B= \left\{2, 6, 9, 14, 18\right\} \C= \left\{\varnothing, 4, 7, 8, 15, 17\right\}$

Find the cardinality of $A\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of A and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$A\cup A = \left\{6, 8, 9, 11, 12, 13\right\}$
Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{4, 12, 20, 25, 28\right\} \B= \left\{\varnothing, 4, 8, 19, 22, 28\right\} \C= \left\{\varnothing, 3, 4, 8, 13, 14\right\}$

Find the cardinality of $B\cap B$

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of B and B .

We simply find the common elements of the two sets, and count the number of elements.

$B\cap B = \left\{\varnothing, 4, 8, 19, 22, 28\right\}$
Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{6, 7, 10, 11, 19, 24\right\} \B= \left\{5, 8, 15, 17, 19, 28\right\} \C= \left\{1, 2, 3, 7, 9, 14\right\}$

Find the cardinality of $A\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and B .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap B = \left\{19\right\}$
Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{3, 4, 9, 10, 11, 16\right\} \B= \left\{2, 7, 10, 15, 16\right\} \C= \left\{\varnothing, 8, 14, 17, 18\right\}$

Find the cardinality of $A\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of A and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$A\cup A = \left\{3, 4, 9, 10, 11, 16\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{3, 8, 10, 21, 27, 29\right\} \B= \left\{5, 10, 11, 18, 21\right\} \C= \left\{\varnothing, 1, 2, 7, 9\right\}$

Find the cardinality of $B\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of B and B .

We simply find the common elements of the two sets, and count the number of elements.

$B\cap B = \left\{5, 10, 11, 18, 21\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{5, 10, 12, 13, 18, 21\right\} \B= \left\{\varnothing, 3, 4, 7, 10, 16\right\} \C= \left\{2, 4, 5, 7, 13\right\}$

Find the cardinality of $A\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and B .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap B = \left\{10\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{11, 12, 13, 14, 18\right\} \B= \left\{1, 10, 11, 14, 16\right\} \C= \left\{3, 6, 8, 10, 17\right\}$

Find the cardinality of $B\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of B and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$B\cup A = \left\{1, 10, 11, 12, 13, 14, 16, 18\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{9, 10, 16, 17, 19\right\} \B= \left\{3, 6, 8, 18\right\} \C= \left\{1, 7, 8, 10\right\}$

Find the cardinality of $A\cup A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the union of A and A .

We simply combine the two sets together, and count the number of elements. If there are any elements that are the same, we keep one of them, and not both.

$A\cup A = \left\{9, 10, 16, 17, 19\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{1, 2, 4, 6, 11, 21\right\} \B= \left\{3, 10, 13, 14, 21, 22\right\} \C= \left\{2, 4, 5, 8, 12, 14\right\}$

Find the cardinality of $A\cap B$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and B .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap B = \left\{21\right\}$

Now we simply count the number of elements in this set.

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Question

If

$\A= \left\{12, 22, 26, 28, 29\right\} \B= \left\{1, 4, 14, 15, 22, 24\right\} \C= \left\{\varnothing, 2, 4, 8, 13, 14\right\}$

Find the cardinality of $A\cap A$ .

Tap to reveal answer

Answer

The question is asking us to find the number of elements in the intersection of A and A .

We simply find the common elements of the two sets, and count the number of elements.

$A\cap A = \left\{12, 22, 26, 28, 29\right\}$

Now we simply count the number of elements in this set.

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