Suppose A={0,12,−3,7,18}, B={−1,5,7,18}, and C={−3,5,9}. What is A∩(B∪C)?

{-3, 7, 18}

Step-by-step explanation:

B ∪ C = {-3, -1, 5, 7, 9, 18}

A ∩ (B∪C) = {-3, 7, 18}

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Step-by-step explanation:

First we look at PEMDAS.

In A∩(B∪C), parentheses come first.

So, we do B∪C.

The ∪ symbolizes union, which means you have to combine the elements of the two sets.

If B={−1,5,7,18}, and C={−3,5,9}, then both of them together is {-3,−1,5,7,9,18}. I used underlining and italics to show where the numbers came from. There is a 5 in both sets, but you only have to put it once.

B∪C={-3,−1,5,7,9,18}.

Now that we have B∪C, we can solve for A∩(B∪C).

∩ means intersection, so you find the elements in both sets. Basically, just look for numbers that appear in both A and B∪C.

B∪C={-3,−1,5,7,9,18}

A={0,12,-3,7,18}

Therefore, A∩(B∪C)={-3, 7, 18}

Hope this helped! <3

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