Let X be a nonempty set and let P(X) denote the collection of all subsets of X. Define f:X\timesP(X)\toR by f(x,A)=\\begin{array}{cc}1{ &\end{array},\if x \inA;0{,},\if x\notinA Then f(x,A\cupB) equals

Correct Answer is : f(x,A)+f(x,B)−f(x,A)f(x,B)

KVPY SB SX Exam 2011 Question Paper

Question : 20 of 120

Marks: +1, -0

Let X be a nonempty set and let P(X) denote the collection of all subsets of X. Define

f:X×P(X)→R

f(x,A)=\{\table 1{,},\if x ∈A;0{,},\if x∉A

Then

f(x,A∪B)

equals

Solution:

f(x,A ∪B)=\{\table 1{,},\if x ∈A∪B;0{,},\if x∉A∪B

\table \if x ∈A,x∈B;\if x ∈A,x∉B;\if x ∉A,x∈B\}⇒\f(x,A∪B)=1

⇒None of the option(A, B, D)satisfy

\if x ∉ A, x ∉ B

⇒\f(x,A ∪B) =0

⇒ C(only C satisfy)

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