In: Computer Science
Use the laws of propositional logic to prove that the following compound propositions are tautologies.
((? → ?) ∧ (? → ?)) → (? → ?)
Ans:-
You should know :-
a ->(implies) b will be false only if a is true and b is false
a^b will be true only if both a is true and b is true
If all cases are true then its tautology
Take all cases.
1 denotes True, 0 denotes False in below table
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bomo : - Here pimplies True, o implies false p q r (eq) ( gr) (6) (169) MG) ( 9 ) / ) (fr) 0 0 0 1 1 o ao a - - ooo o - --0- --- - oo ---- o - --0-OOO- -- -0-0- 1 1 0 0-