# 1 s l s l t t t t f f f t t f f t 2 d l s d l d l d s

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1.  S L S L T T T T F F F T T F F T 2.  D L S D (L  D) (L  D) S T T T F F T T T F F F T T F T F F T T F F F F T F T T T T T F T F T T F F F T T F T

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F F F T F T 3.  S D D ( D S) S ( D S ) T T F T T T F T T T F T F T T F F T F T 4. D L S S L (D  L) S (D  L) T T T F F T T T T F T F T T T F T F T T T T F F T T T T F T T F F F T F T F T F F F F F T F T T T F F F T T T T C. Identify which  two  of the four compound propositions in part A are logically  equivalent. 1. Explain how you know the two propositions are logically equivalent. a. Statements 2&4 are logically equivalent.  b. Statements 2&4 are logically equivalent due to DeMorgan’s Law, which negates the  ” within  (L  D) S with the “ ” within  S (D  L), thus allowing  (L  D) S and  S (D  L) to be logically equivalent. D L S (L  D) S S (D  L) T T T T T T T F T T T F T T T T F F T T F T T T T
F T F F F F F T T T F F F T T D. Explain what a tautology is, using the properties of logic. 1. Identify which, if any, of the four compound propositions in part A is a tautology. a. Planetmath.org defines a tautology as “a statement which is true regardless of the  truth value of the substatements of which it is composed” (planetmath.org, 2013).

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• Spring '17
• Irani

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