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If X and Y are two sets such that X Y has 18 elements, X has

Question

If X and Y are two sets such that $X \cup Y$ has $18$ elements, X has $8$ elements and Y has $15$ elements; how many elements does $X \cap Y$ have?

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Lucas Discussed

If X and Y are two sets such that

X \cup Y

has

18

elements, X has

8

elements and Y has

15

elements; how many elements does

X \cap Y

have?

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

It is given that:

n (X \cup Y) = 18, n (X) = 8, n (Y) = 15

n (X \cap Y) = ?

We know that:

n (X \cup Y) = n (X) + n (Y) - n (X \cap Y)

∴ 18 = 8 + 15 - n (X \cap Y)

\Rightarrow n (X \cap Y) = 23 - 18 = 5

∴ n (X \cap Y) = 5

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Question Text	If X and Y are two sets such that $X \cup Y$ has $18$ elements, X has $8$ elements and Y has $15$ elements; how many elements does $X \cap Y$ have?
Answer Type	Text solution:1
Upvotes	150