Question

Which of the sets shown includes the elements of set Z that are both odd numbers and multiples of 7? Z = {−21, −14, −7, 0, 7, 14, 21}

Answer 1

Answer:

B. {−21, −7, 7, 21}

Step-by-step explanation:

Choices for this question are

A. {−21, 21}

B. {−21, −7, 7, 21}

C. {−14, 0, 14}

D. {−21, −14, −7}

We need to pick a set that has elements of Z and they are odd number and multiples of 7.

Therefore, the right answer is

B. {−21, −7, 7, 21}

Because, this set includes all elements of set Z that are odds and multiples of 7.

The choice A doesn't include -7 and 7, which has to.

Choice C and D includes even numbers.

Answer 2

The set that has elements of set Z that are odd numbers and are also a multiple of 7 is:

{−21, −7, 7, 21}.

Let's recall what an odd number that is a multiple of 7 is:

• An odd number is an integer that you cannot divide into two without a remainder.

• If you divide an odd number by 2, you will always have a remainder

• A multiple of 7 is any number you will get when you multiply 7 and another number.

• Let's consider the given set of Z:

Z = {-21, -14, -7, 0, 7, 14, 21}

In the set given we have the following:

• -21, -7, 7, 21 are all odd numbers

• -21, -14, -7, 7, 14, and 21 are all multiples of 7.

However, -21, -7, 7, and 21 are all both multiples of 7 and also are odd numbers.

Therefore, the set that has elements of set Z that are both odd numbers and are also multiples of 7 is:

{−21, −7, 7, 21}

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