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If p and q are true propositions, while r and s are false propositions, what is the truth value of the expression ~ [(p ∨ ~r) ∨ (~q ∨ s)]?

1. true
2. false
3. false if p is true
4. None of these

Correct answer: false

Solution

With p=T,q=T,r=F,s=F: p v ~r = T v T = T, so (p v ~r) v (~q v s) = T. Negation gives F. The expression is false.

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