Mathematics, 20.02.2020 06:35 AK3892
About Exercise 2.3.1: Proving conditional statements by contrapositive Prove each statement by contrapositive
a. For every integer n, if n2 is an odd, then n is odd. Solution
b. For every integer n, if n is even, then n is even
c. For every integer n, if 5n +3 is even, then n is odd.
d. For every integer n, if n2 2n 7 is even, then n is odd
e. For every real number r, if is irrational, then - is also irrational.
f. For every non-zero real number az, if z is irrational, then 1 is also irrational.
g. For every pair of real numbers x and y, lf Z3 + Xy2-ry + y3, then z < y
h. For every integer n, if n2 is not divisible by 4, then n is odd.
i. For every pair of real numbers z and y. if +y is irrational, then z is irrational or y is irrational.
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