Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it: a. The inequality 2^x >= x + 1 is true for all positive real numbers x. b. Suppose A, B, and C are sets. If A = B - C, then B = A intersect C. c. There exists integers a and b for which 42a + 7b = 1. d. If X is a subset of A U B,then X is a subset of A or X is a subset of B.
Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it: a. The inequality 2^x >= x + 1 is true for all positive real numbers x. b. Suppose A, B, and C are sets. If A = B - C, then B = A intersect C. c. There exists integers a and b for which 42a + 7b = 1. d. If X is a subset of A U B,then X is a subset of A or X is a subset of B.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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Question
Each of the following statements is either true or false. If a statement is true, prove
it. If a statement is false, disprove it:
a. The inequality 2^x >= x + 1 is true for all positive real numbers x.
b. Suppose A, B, and C are sets. If A = B - C, then B = A intersect C.
c. There exists integers a and b for which 42a + 7b = 1.
d. If X is a subset of A U B,then X is a subset of A or X is a subset of B.
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