Question

In: Computer Science

X(Y'+Z)+[X(Y'+X)]'=1 State which of the following theorems is used to simplify A) Idempotent B) Law of...

X(Y'+Z)+[X(Y'+X)]'=1 State which of the following theorems is used to simplify A) Idempotent B) Law of Complementary C) Operations involving 1&0 D) Involution

Expert Solution

Answer: Options

B) Law of Complementary

D) Involution

Explanation:

Given X(Y'+Z)+[X(Y'+X)]'=1

X(Y'+Z)+[X'+(Y'+X)'] =1 { Law of Complementary (PQ)'= P'+ Q' }

X(Y'+Z)+[X'+((Y')'X')] =1 { We know that (P+Q)'= P' Q' }

 (XY'+XZ)+[X'+(YX')] =1{ Involution Law Y = (Y')' }

 (XY'+XZ)+[X'(1+Y)]=1 { By Distributive law PQ+PR = P(Q+R) }

 (XY'+XZ)+[X'(1)] =1 { We know that P+1= 1 }

 (XY'+XZ)+X'=1 { We know that P(1)= P }

 XY'+(XZ+X') =1 { Associative law}

 XY'+(X+X')(Z+X') =1 { By Distributive law P+QR = (P+Q)(P+R) }

 XY'+(1)(Z+X') =1 { We know that P+P'= 1 }

 XY'+Z+X' =1

 XY'+X'+Z =1 { Commutative law P+Q = Q+P}

 (X+X')(Y'+X')+Z =1{ By Distributive law P+QR = (P+Q)(P+R) }

 (1)(Y'+X')+Z =1 { We know that P+P'= 1 }

 Y'+X'+Z =1

Which is Required simplified Expression

venereology answered 1 year ago

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