Question

Paul 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 4}. List the outcomes in A ∪ B.

{4, 8, 12}

{3, 4, 5, 7, 8, 9, 11, 12}

{3, 5, 7, 9, 11}

{ }

Answer 1

I think the correct answer among the choices listed above is the second option. From the given statement, the values of A and B should be:

A = {3, 5, 7, 9, 11}
B = {4, 8, 12}

Then,

A ∪ B = {3, 4, 5, 7, 8, 9, 11, 12}

Answer 2

2. A ∪ B = {3,4,5,7,8,9,11,12}

Explanation:

We are given that,

Paul rolls two number cubes each numbered {1,2,3,4,5,6}.

Then the outcomes are of the type (x,y) where x,y belongs to {1,2,3,4,5,6}.

Then, the possible outcomes for
`x+y` = {2,3,4,5,6,7,8,9,10,11,12}

Since, A = {the sum of the number cubes is odd}

So, the possible outcomes for the odd sum = {3,5,7,9,11}

Also, B = {the sum of the number cubes is divisible by 4}.

So, the possible outcomes for the sum divisible by 4 = {4,8,12}

It is required to find the outcomes in A ∪ B.

A ∪ B = The set where the sum of numbers is either odd or divisible by 4.

i.e. A ∪ B = {3,4,5,7,8,9,11,12}

Thus, option 2 is correct.