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Concept explainers
Let T be the statement: The sum of any two rational numbers is rational. Then T is true but the following “proof” is incorrect. Find the mistake.
“Proof” by contradiction: Suppose not. That is, suppose that the sum of any two rational numbers is not rational. This means that no matter what two rational numbers are chosen their sum is not rational. Now both 1 and 3 are rational because 1=1/1 and
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Chapter 4 Solutions
Discrete Mathematics With Applications
- Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation can be proved to be true for n=k+1. Explain why this does not prove that the statement is true for all positive integers. Is the statement true for all positive integers? Why?arrow_forwardProve that 23 is not a rational number.arrow_forwardWhen can a theorem be cited as a reason reason in a proof?arrow_forward
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