11. If n(a) = 40, n(A) = 20, n(B') = 16 and n(AUB) = 32, then find n(B) and n(
A
B).
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Answer:
Step-by-step explanation:
Given : n ( A ) = 25 ; n ( B ) = 40 ; n ( A U B ) = 50 ; n ( B¹ ) = 25
Formula to be used : n ( A U B ) = n ( A ) + n ( B ) - n ( A ∩ B )
Substituting the given values in the above formula we get,
=> 50 = 25 + 40 - n ( A ∩ B )
=> n ( A ∩ B ) = 25 + 40 - 50
=> n ( A ∩ B ) = 65 - 50 = 15
Hence n ( A ∩ B ) = 15
We also know that,
n ( B¹ ) = n ( U ) - n ( B )
Substituting the values we get,
25 = n ( U ) - 40
=> n ( U ) = 40 + 25 = 65.
Hence the universal set n ( U ) contains 65 elements.
HERE IS AN EXAMPLE TRY IT YOURSELF
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