Problem 4.8

Let D = {48, 14, 8, 0, 1, 3, 16, 23, 26, 32, 36}.

Determine which of the following propositions are true and which are false. Provide counter examples for those propositions that are false.

a. x D, if x is odd then x > 0.

b. x D, if x is less than 0 then x is even.

c. x D, if x is even then x 0.

d. x D, if the ones digit of x is 2, then the tens digit is 3 or 4.

e. x D, if the ones digit of x is 6, then the tens digit is 1 or 2

Problem 4.9

Write the negation of the proposition :x IR, if x(x + 1) > 0 then x > 0 or x - 1. For each x given below, find an n to make the predicate n > x true.

a. x = 15.83

b. x = 108c. x = 101010.