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1) Decide which of the following are propositions (YN) and give the truth value

ID: 3195497 • Letter: 1

Question

1) Decide which of the following are propositions (YN) and give the truth value a) 127 is an even integer b) All triangles have 4 sides or more 2) Negate the following statements, using full sentences a) John 1s smarf or Fred 1s not tall b) Some animals are intelligent 3) Is (P-Q)-to(P Q) ? (Q means not Q.stands for equivalent). Justify your answer 4) Given the proposition P(n) If n3 is odd then n is odd" a) Prove P(n) by contraposition: b) Prove P(n) contradiction: 5) Prove by induction: 12 2232n2 - , n 21 6) Using the predicate symbols shown and appropriate quantifiers, write each English Language statement in symbolic form (The domain is the whole world) J(x) is "x is a judge" C(x) is "x is a chemist" W(x) is "x is a woman L(x) is "X is a lawyer" Ax, y) is "x admires y', a) There are some women lawyers who are chemists b) No woman is both a lawyer and chemist. c) Some lawyers admire only judges d) All women lawyers admire some judges e) Some women admire no lawyer

Explanation / Answer

Sentences considered in propositional logic are not arbitrary sentences but are the ones that are either true or false, but not both. This kind of sentences are called propositions.

a) the given sence is proposition as it is either true or false.

FALSE as 127 is an odd integer.

b) the given sence is proposition as it is either true or false.

FALSE as all triangles have 3 sides.