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Unformatted text preview: ∼ on Z as follows: a ∼ b if and only if 3 a + b is a multiple of 4. Prove that ∼ is an equivalence relation. 5 [5 points] Question 6. Suppose our universe of discourse is the set of all cats. Let S ( x ) be the predicate “ x loves salmon” Let T ( x ) be the predicate “ x is teachable” Let M ( x ) be the predicate “ x is missing a tail” Let W ( x ) be the predicate “ x has whiskers” Let G ( x ) be the predicate “ x has green eyes” Let K ( x ) be the predicate “Koko the gorilla likes to play with x ” Let F ( x,y ) be the predicate “ x is willing to ﬁght with y .” Express each of the following as English sentences. ∃ x ( ¬ W ( x ) ) ∀ x ( M ( x ) → K ( x ) ) ∀ x ( G ( x ) → ∃ y F ( y,x ) ) ∀ x ± W ( x ) → ( S ( x ) → T ( x ) ) ² ∀ x ± S ( x ) → ∃ y ( ¬ F ( x,y ) ∧ ¬ F ( y,x ) ) ² 6...
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 Spring '08
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 Math, Logic, True, Proposition, Logical connective

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