MAT137Y1 Lecture Notes - Lecture 4: Rational Number
MAT137Y1 verified notes
4/39View all
Document Summary
Let a = {2,3,4} for all x in a, x > 0: For all x that exists in integer numbers, x > 0. This is false as if we take x = -6, then -6 is a integer, but -6 < 0, so this is false. For example, consider the following four quantified statements: For all integers x, 1x is a rational number. There exists an integer x such that x is even. There exists a real number x such that 1x = 0. The first statement is true because its claim that 2x + 2 = 2(x + 1) is indeed true for every real number x. An implication is a statement of the form if a, then b (also written a . Such an implication is true if, whenever statement a is true, statement b must also be true. The converse of the implication a b is the implication b a.
