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HW2Solution

# HW2Solution - Homework#2 Suggested Solution Section 2.1...

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Homework #2 Suggested Solution

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Section 2.1, Exercise 3 (not homework problem, just for review) Provide Counterexamples to the following statement Every geometric figure with four angles is a square Counterexample: a rectangle If a real number is not positive, then it must be negative Counterexample: 0 All people with red hair have green eyes or are tall Counterexample: one with red hair but not green eyes nor tall All people with red hair have green eyes and are tall Counterexample1: one with red hair but no green eyes Another example: one with red hair but short
Section 2.1, Exercise 4 Provide counterexamples to the following statements The number n is an odd integer if and only if 3n+5 is an even integer If n is an odd integer, then 3n+5 is an even integer (this part is true, so we can’t find a counterexample) If 3n+5 is an even integer, then n is an odd integer (this part is not true, an counter example is: 3n+5 = 6, an even integer, but in this case, n=1/3, not an integer at all!) The number n is an even integer if and only if 3n+2 is an even integer Similar to above, if 3n+2 is an even integer, say 6, n=4/3, not an integer at all.

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