Question

Use the Venn Diagram in #1 to answer the following question: How many elements are contained in B ∪ C ?

Answer 1

Answer: D) 63

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Work Shown:

The notation B U C means "set B or set C". The U refers to set union. A set union is where you combine two sets and toss out any duplicates. In terms of a venn diagram, we will add up any number that is either in set B, set C, or both sets at the same time.

So we just add up the numbers: {6, 19, 5, 8, 3, 22} to get

6+19+5+8+3+22 = 63

There are 63 items in either set B, set C or both.

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Alternative route:

n(B) = number of items in set B

n(B) = 6+19+5+8 ... add up the numbers in circle B

n(B) = 38

n(C) = number of items in set C

n(C) = 3+5+8+22

n(C) = 38

n(B and C) = number of items in both set B and set C

n(B and C) = 5+8

n(B and C) = 13

n(B U C) = n(B) + n(C) - n(B and C)

n(B U C) = 38 + 38 - 13

n(B U C) = 63