Question

Use the given sets to find A U B

A={3,4,5,6,7,8,9,10,11}
B={7,9,11,13,15,17}

Answer 1

Answer: {3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17}

Step-by-step explanation:

The U means "union" for "set union"

Imagine you have two bins of blocks. Bin A has blocks labeled with 3, 4, 5, etc etc as shown. Bin B has 7, 9, 11, etc etc.

The union of two sets is simply taking those two bins and tossing them together into one larger bin. We combine the two sets so to speak. We don't add the values. We just list all the values shown. If Bin C is the union of Bin A and Bin B, then the block comes from either bin A or B (or both).

Keep in mind that we toss out duplicates. Also, this is optional, but we can write the values in order from smallest to largest.

In the answer above, The values from 3 to 11 are from bin A (with 7,9,11 from bin B too). Note how I don't list 7, 9 or 11 twice. After 11 is 13,15,17 which are exclusively in set B.

side note: you can think of "union" as in "marriage". When two people get married, they combine their stuff together. So for example, the couple will combine their movie collection but they will likely toss out any duplicates (why have two copies of the same movie?). For bigger items such as sofas, it is more likely to toss out a duplicate unless there's extra space. But just imagine that this is a small apartment.

Answer 2

Answer: {3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17}

Step-by-step explanation:

A U B means the union of set A and set B. So, if we join them together, we get everything that is in set A and everything that is in set B:

3, 4, 5, 6, 7, 8, 9, 10, 11 and 7, 9, 11, 13, 15, 17

= 3, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 13, 15, 17

Notice that 7, 9, and 11 are in both set A and set B but we only need to list them once.

BONUS: A similar example:

Fruit Salad A contains: {apples, oranges, watermelon, and bananas}

Fruit Salad B contains: (blueberries, strawberries, bananas, and apples}

If I mix them together (A U B), the Fruit Salad will contain: {apples, oranges, watermelon, and bananas, blueberries, and strawberries).

We do not have to list the apples and bananas again.