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# 210hw1 - p x has at least one root(iii A linearly...

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Math 210 Homework 1 Due Friday February 18th 1. Classify each of the following statements as true or false. (i) 3 3 is rational or ( - 4) 2 = 16 (ii) 4 = 2 + 2 7 < 50 (iii) 4 6 = 2 + 2 7 < 50 (iv) 4 6 = 2 + 2 7 > 50 (v) 4 = 2 + 2 7 > 50 2. Rewrite each statement so that it is clear that it is an implication. (i) To be President, you must be at least 35. (ii) A matrix with nonzero determinant is invertible. (iii) The product of two irrational numbers is irrational. 3. State the converse and the contrapositive of each statement. (i) Every square is a polygon with four sides. (ii) If p ( x ) is a polynomial of odd degree, then
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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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