# Introduction to Proofs : Functions, Relations, & Cardinality

## Example Questions

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### Example Question #1 : Functions, Relations, & Cardinality

If

Find the cardinality of

Explanation:

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.

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

### Example Question #2 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #3 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #4 : Intro To Proofs

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #4 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #5 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #6 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #7 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #8 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

### Example Question #9 : Functions, Relations, & Cardinality

If

Find the cardinality of .

Explanation:

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.

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

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