Unformatted text preview: p ( x ) has at least one root. (iii) A linearly independent set of vectors contains at most n vectors. 4. Rewrite each statement using the quantiﬁers ∀ and ∃ as appropriate. (i) If x is a real number, then e x is positive. (ii) An integer cannot be both even and odd. (iii) Given any prime number, there is another prime number that’s bigger. 5. Give a counterexample to each statement. (i) ( x-3) 2 = x-3 → x = 3. (ii) The product of two irrational numbers is irrational. 1...
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- Spring '08
- Math, Rational number, Complex number