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Question. Name the law given and verify it using a truth table. X+ X’.Y=X+Y
My Answewr give below

X | Y | X’ | X’.Y | X+X’.Y | X+Y
0 | 0 | 1  | 0    | 0      | 0
0 | 1 | 1  | 1    | 1      | 1
1 | 0 | 0  | 0    | 1      | 1
1 | 1 | 0  | 0    | 1      | 1
Prove algebraically that X + X’Y = X + Y.
L.H.S. = X + X’Y
           = X.1 + X’Y         (X . 1 = X property of 0 and 1)
           = X(1 + Y) + X’Y    (1 + Y = 1 property of 0 and 1)
           = X + XY +  X’Y                                                            
           = X + Y(X + X’)
           = X + Y.1           (X + X’ =1 complementary law)
           = X + Y             (Y . 1 = Y property of 0 and 1)
           = R.H.S.      Hence proved.

My teacher marked my answer WRONG. And told me to find the correct answer. Friends tell me is it a complementary law or distributive law or Absorption law? If it is absorption kindly tell me how to prove RHS and LHS algebraically.

Thank you for any advice or suggestions.

Edited by vishalonne
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  • Latest Post Latest Post by faroukmuhammad

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Short answer: the identity X + X'Y = X + Y is commonly taught as the redundancy (or reduction) law; it’s also the simple/special-case form of the consensus/redundancy idea used in logic minimization. ’s short name is essentially correct, and ’s truth table and final result are right — the likely issue from your teacher was the exact name expected and a concise justification. (geeksforgeeks.org)

How to state it cleanly in an answer: name it “redundancy (reduction) law” and give a one-line algebraic justification plus the truth table for verification. One standard one-line approach is to apply the distributive identity to form a product-of-sums and then use the complement law to collapse a factor to 1, leaving X + Y; alternatively, a short case argument also works (if X=1 the whole sum is 1; if X=0 the expression reduces to Y). Either presentation is accepted in exams and in textbooks. (testbook.com)

Quick exam tip: write the law name exactly (teacher may expect “redundancy” or “reduction”), show the 4-row truth table (you already did this correctly), then add the compact algebraic justification (product-of-sums line or two-line case analysis). Mentioning that this identity is used to drop redundant terms when minimizing circuits (K‑maps or algebraic simplification) shows understanding and usually satisfies graders. (natalieagus.github.io)

Member Avatar for faroukmuhammad

Redundace Law . Your proof is right by the way.

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