GATE | GATE-CS-2006 | Question 27
Consider the following propositional statements: P1 : ((A ∧ B) → C)) ≡ ((A → C) ∧ (B → C)) P2 : ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C)) Which one of the following is true?
P1 is a tautology, but not P2
P2 is a tautology, but not P1
P1 and P2 are both tautologies
Both P1 and P2 are not tautologies
The easiest way to solve this question is by creating truth tables for the expressions given. Note that P1 will be a tautology if truth table for left expression is exactly same as truth table for right expression. Same holds for P2 also.
|A||B||C||((A ∧ B) → C))||((A → C) ∧ (B → C))||((A ∨ B) → C))||((A → C) ∨ (B → C))|
So as we see from table, none of the P1 or P2 are tautologies, so option (D) is correct. Source: www.cse.iitd.ac.in/~mittal/gate/gate_math_2006.html
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