The Boolean expression (x + y)(x + bar y) + bar((x + y) + x) simplifie

1.	The Boolean expression (x + y)(x + bar y) + bar((x + y) + x) simplifies to(A) X(B) Y(C) XY(D) X + Y
Answer» Correct option (A) X Explanation: Given Boolean Expression is (x + y)(x + bar y)+ bar(xy + x) As per the transposition theorem (A + BC) = (A + B)(A + C) So, (x + y)(x + bar y) = x + y bar y = x + 0 (x + y)(x + bar y) + bar (xy + x) = x + bar(xy).x = x + (bar x + y).x = x + bar xx + y.x = x + 0 + y.x Apply absorption theorem = x(1 + y) = x.1 = x

The Boolean expression (x + y)(x + bar y) + bar((x + y) + x) simplifies to(A) X(B) Y(C) XY(D) X + Y

Answer»

Correct option (A) X

Explanation:

Given Boolean Expression is (x + y)(x + bar y)+ bar(xy + x)

As per the transposition theorem

(A + BC) = (A + B)(A + C)

So, (x + y)(x + bar y) = x + y bar y = x + 0

(x + y)(x + bar y) + bar (xy + x) = x + bar(xy).x

= x + (bar x + y).x = x + bar xx + y.x = x + 0 + y.x

Apply absorption theorem = x(1 + y) = x.1 = x

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The Boolean expression (x + y)(x + bar y) + bar((x + y) + x) simplifies to(A) X(B) Y(C) XY(D) X + Y

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