Single Choice

In the Venn diagram, the numbers represent the number of elements in the subsets. Given that $$\xi = F\cup G\cup H$$ and $$n(\xi) = 42$$, find $$n(G'\cup H)$$

A$$18$$
B$$28$$
C$$30$$
Correct Answer
D$$38$$

Solution

$$n(\xi) = 42$$

$$n(G) = 12, n(F) = 17, n(H) = 8$$

$$n(F \cap G) = 5, n(G \cap H) = 0, n(F \cap H) = 0$$

$$n(G’)= 42-7-5 =30$$

$$n(H)= 8, n(G’ \cup H) = n(G')+n(H)-n(G'\cap H)=30+8-8 = 30$$

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