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.

The batch 3,5,7,9,11 represents items in set A which are the sums that are odd. For instance, rolling a 2 and a 3 leads to 2+3 = 5 which is an odd number sum.

The batch 4,8,12 represents the sums that are divisible by 4, ie they are multiples of 4. For instance: 2+6 = 8 is a multiple of 4.

The notation A U B means "A union B". Set union has us combine the two sets together to form one single set as indicated above. We toss out any duplicate entries. In this case, there are no duplicates because sets A and B have nothing in common. This means sets A and B are disjoint or mutually exclusive. If an item is in set A, then it cannot be in set B, and vice versa.

Optionally you can sort the items from smallest to largest getting A U B = {3,4,5,7,8,9,11,12}, but I chose to list 3,5,7,9,11 first to show that those items all belonged originally to set A, and kept 4,8,12 separate as well.

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3