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KVPY2011MathematicsSets and Relations

Let X be a nonempty set and let P(X) denote the collection of all subsets of X . Define array l f: X P(X) R by f(x, A)= array ll 1, & if x A 0, & if x A array . array Then f(x, A B) equals -

Options

  1. Af(x, A)+f(x, B)
  2. Bf(x, A)+f(x, B)-1
  3. Cf(x, A)+f(x, B)-f(x, A) f(x, B)
  4. Df(x, A)+|f(x, A)-f(x, B)|

Correct answer

C. f(x, A)+f(x, B)-f(x, A) f(x, B)

Step-by-step solution

f(x, A B)= array lll 1 & if & x A B 0 & if & x A B array . if x A , x B f ( x , A B )=0 C (only C satisfy)

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