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Which of the following is a tautology? 

Option: 1

(P and Q) or (not P and Q) 


Option: 2

P implies (not P) 


Option: 3

P iff (P and Q) 


Option: 4

(P or not P) and (Q or not Q)


Answers (1)

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A tautology is a compound proposition that is always true, regardless of the truth values of its constituent propositions. 

Option (4) is correct as in this case, the tautology is the compound proposition (P or not P) and (Q or not Q), which is always true because it includes all possible combinations of truth values for P and Q. 

Option (1) is incorrect as this compound proposition is not a tautology, because it is only true when both P and Q have the same truth value (either both true or both false). 

Option (2) is incorrect as this compound proposition is not a tautology, because it is only true when P is false (in which case, the antecedent is true and the consequent is also true). 

Option (3) is incorrect as this compound proposition is not a tautology, because it is only true when P and Q have the same truth value (either both true or both false).

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