In each case, justify your answer: if the answer is yes, give a metalogic proof; if the answer is no, give a counterexample. 4. Do the formulas P and P Q in... → Q together semantically imply the formula (a) ...Łukasiewicz's system? (b) ... Kleene's? (c) ...the logic of paradox? (d) ...the system of supervaluations?

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A: .

Q: DeMorgan's Laws

A: We have to use the De Morgan's Laws

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A: We know , (a/b)n = an/bn

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Q: What is the symbolic statement, symbloic negation and verbal negation of "Some dog is small and…

A: Variable:  A variable is a symbol for an element in a collection or set Quantifiers: It refers to…

Q: write the contrapositive of: "if the earth is red, then the sky is black."

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