Question

Stephanie is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is odd} and let B = {the sum of the number cubes is divisible by 3}. List the outcomes in A ∩ B. (5 points)

Answer 1

A ∩ B = {3,9}

Explanation:

Consider the completer question is "Stephanie is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is odd} and let B = {the sum of the number cubes is divisible by 3}. List the outcomes in A ∩ B. Options : {1,3,5,7,9,11} , {1,3,9} , {3,9}, {3,9,12}"

It is given that Stephanie is playing a board game and rolls two number cubes.

Let A = {The sum of the number cubes is odd}

A = {3,5,7,9,11}

B = {The sum of the number cubes is divisible by 3}

B = {3,6,9,12}

We need to find the outcomes in A ∩ B.

It means we need to find the common elements of A and B.

A ∩ B = {3,9}

Therefore, the required set of values is {3,9}.

Answer 2

A ∩ B = {3, 9}

Explanation:

First we find the possible values for the set A.

By launching the number cubes you can only get numbers from 1 to 6

You can get:

`A = \{3, 5, 7, 9, 11\}`

For set B you can get:

`B = \{3, 6, 9, 12\}` The numbers that are divisible by 3

The set A ∩ B will be formed by the elements that are in A and are also in B. In this case they are: the odd numbers that are divisible by 3

Finally we have that:

A ∩ B = {3, 9}