Prove using deductive reasoning the following conjectures. If the conjecture is FALSE, give a counterexample. 1. Prove that the negative of any even integer is even. 2. Prove that the difference between an even integer and an odd integer is even. 3. Prove that the sum of three consecutive integers is always a multiple of 3. 4. Prove that the difference between the square of any odd integer and the integer itself is always an even integer. MWPrackice Set 5. Prove that the sum of a two digit number and its reversal is a multiple of 11.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: 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...
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Prove using deductive reasoning the following conjectures. If the conjecture is FALSE, give a
counterexample.
1. Prove that the negative of any even integer is even.
2. Prove that the difference between an even integer and an odd integer is even.
3. Prove that the sum of three consecutive integers is always a multiple of 3.
4. Prove that the difference between the square of any odd integer and the integer itself is always an
even integer.
MWPrackice Set
5. Prove that the sum of a two digit number and its reversal is a multiple of 11.
Transcribed Image Text:Prove using deductive reasoning the following conjectures. If the conjecture is FALSE, give a counterexample. 1. Prove that the negative of any even integer is even. 2. Prove that the difference between an even integer and an odd integer is even. 3. Prove that the sum of three consecutive integers is always a multiple of 3. 4. Prove that the difference between the square of any odd integer and the integer itself is always an even integer. MWPrackice Set 5. Prove that the sum of a two digit number and its reversal is a multiple of 11.
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