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Let X be be a ninempty set and let P(X) ...

Let X be be a ninempty set and let P(X) denote the collection of all subsets of X. Define
`f : X xx P(X) rarr` by
`f(x, A)={(1",",if,x in A),(0",",if,x notin A):}`
Then `f(x, A uu B)` equals-

A

`f(x, A)+f(x, B)`

B

`f(x, A)+f(x, B)-1`

C

`f(x, A)+f(x, B)-f(x, A) f(x, B)`

D

`f(x, A)+|f(x, A)-f(x, B)|`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x, A uuB)={(1,if,x in A uu B),(0,if,x notin A uu B):}`
`{:(if,x in A",",x in B),(if,x in A",",x notinB),(if,x notin A",",x in B):}} {:(rArr f(x, A uu B)=1rArr" None of the option (A, B, D) satisfy"),(),():}`
if `x notin A, x notin B rArr f(x, A uu B)=0 rArr C("only C satisfy")`
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