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If (i) A = 1, B = 0, C = 1, (ii) A = B =...

If (i) `A = 1, B = 0, C = 1, (ii) A = B = C = 1, (iii) A = B = C = 0 and (iv) A = 1 = B, C = 0` then which one of the following options will satisfy the expression, `X=bar(A.B.C)+bar(B.C.A)+bar(C.A.B)`

A

(1, 0, 1, 1)

B

(1, 0, 1, 0)

C

(0, 1, 1, 1)

D

`(1, 1, 1, 0)

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `X=bar(A.B.C)+bar(B.C.A)+bar(C.A.B)`
For (i) `A.B.C=B.C.A=C.A.B=0`
And `bar(A.B.C)=bar(B.C.A)=bar(C.A.B)=1`
`"So "X=1+1+1=1`
For (ii) A.B.C = B.C.A = C.A.B = 1
`bar(A.B.C)=bar(B.C.A)=bar(C.A.B)=1`
`"So "X=0+0+=0`
For (iii) `A.B.C=B.C.A=C.A.B=0`
`bar(A.B.C)=bar(B.C.A)=bar(C.A.B)=1" "therefore" "x=bar(A.B.C)+bar(B.C.A)+bar(C.A.B)=1+1+1=1`
For (iv) `A.B.C=B.C.A=C.A.B=0`
`bar(A.B.C)=bar(B.C.A)=bar(C.A.B)=1" "therefore" "x=1+1+1=1`
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