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KCET2019MathematicsSets and Relations

If ( U ) is the universal set with ( 100 ) elements; ( A ) and ( B ) are two sets such that ( n(A)=50, n(B)=60 ), ( n(A B)=20 ) then ( n (A^ B^ )= )

Options

  1. A( 20 )
  2. B( 10 )
  3. C( 40 )
  4. D( 90 )

Correct answer

B. ( 10 )

Step-by-step solution

(B)n(U)=100n(A)=50n(B)=60n(A B)=20n(A B)=n(A)+n(B)-n(A B)=50+60-20=110-20=90n (A^ B^ )=n(A B)^ =n(U)-n(A B)=100-90=10

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