Question

1. Determine whether the following statements are true or false.

If they are true to prove them if they are false to provide a counterexample.

(a) The difference between any two odd integers is even.

(b) If ???? and ???? are integers and ???? +???? is even, then either ???? is even or ???? is even.

(c) If ???? is odd and ???? is even, then ???? + ???? is odd.

Answer 1

Explanation:

a) True. Let I integer = 2m+1 and second integer 2n+1

Difference = 2(m-n) hence even

b)False. If m and n are integers and m+n is odd then either both even or both odd

Eg: 3 and 5. 3+5 =8 is even but both are even

c) True

m is odd then m= 2n+1

l is even so l = 2p

Sum = 2(n+p)+1 hence odd