Set 4.6: 12, 16, 28 (Prove by Contradiction)
Prove each statement in 10-17 by contradiction.
12. If a and b are rational numbers, b does not equal 0, and r is an irrational number, then a + br is irrational.
16. For all odd integers a, b, and c, if z is a solution of ax^2 + bx + c = 0 then z is irrational. (In the proof, use the properties of even and odd integers that are listed in Example 4.2.3.)
Prove each of the statements in 23-29 in two ways: (a) by contraposition and (b) by contradiction.
28. For all integers m and n, if mn is even then m is even or n is even.
(Per the assignment instructions, I will only be solving by contradiction)
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