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Let X = A . bar (BC) . Evaluate X for ...

Let `X = A . bar (BC)` . Evaluate X for
(a) `A = 1 , B = 0 , C = 1`, (b) A = B = C = 1 and ( c) A = B = C = 0.

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=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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