Unformatted text preview: is odd) ∨ ( b is odd) . In words this is just ‘a is odd or b is odd.’ or ‘a or b is odd.’ (# 2.48) Determine the truth value of each of the following statements. (b) ∀ n ∈ N , n + 1 ≥ 2. (d) ∃ x ∈ R , 3 x 227. Solution . (b) This is a true statement. Note that N is just the set of positive integers { 1 , 2 , 3 , . . . } . Thus if n ∈ N then n ≥ 1 is true. Thus adding 1 to each side of the inequality n + 1 ≥ 1 + 1 = 2 is true for all n ∈ N . (d) This is a true statement. Note that if x = 3 then 3(3) 2 = 3 · 9 = 27. Thus there exists a real number which satisﬁes 3 x 2 = 27. 1...
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 Spring '09
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 Math, Natural number, Proposition

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