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The only statement among the following that is a tautology is:
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a
A∧(A∨B)
b
A∨(A∧B)
c
[A∧(A→B)]→B
d
B→[A∧(A→B)]
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Correct option is C
Note thatA∧(A∨B) is F when A=F, A∨(A∧B) is F when A=F,B=F, and B→[A∧(A→B)] is F when A=F,B=T∴ We check only (c) [A∧(A→B)]→B≡[A∧(~A∨B)]→B≡[(A∧(~A))]∨(A∧B)]→B≡A∧B→B≡~(A∧B)∨B≡∼[(A∧B)∧(~B)]≡~[A∧(B∧~B)]≡∼[A∧F]≡∼F≡TThus,[A∧(A→B)]→B is a tautology.
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