Each of the following statements is either true or false. Determine for eachone whether it is true or false, if it is true prove it and if it is false disproveit (that is, prove its negation).a. Let a, b e Z. If 3 ab then 31(a + b).b. Let n, k, l € Z. If n+k+1 = 101 then two of these integers have oppositeparity.c. Let n € Z. If 3 n and 2n then there exists k EZ such that n = 6k+3.d. There exists an odd integer, the sum of its digits are even and theproduct of its digits are odd.e. There exists a, b, c € Z such that 2a, 4a and a = b²c².f. Let a be a 3-digit integer. Then 3 divides a if and only if 3 divides thesum of the digits of a.g. For every integer n, if 12|n² then 12 n.h. There exist n, m € N such that m² +m + 1 = n².i. There exist n, m EN such that m² +2m = n² - 2n.

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Each of the following statements is either true or false. Determine for each one whether it is true or false, if it is true prove it and if it is false disprove it (that is, prove its negation). a. Let a, b Z. If 3 ab then 31(a + b). b. Let n, k, l € Z. If n+k+1 = 101 then two of these integers have opposite parity. c. Let n € Z. If 3|n and 2 n then there exists k € Z such that n = 6k+3. FRI

Each of the following statements is either true or false. Determine for each one whether it is true or false, if it is true prove it and if it is false disprove it (that is, prove its negation). a. Let a, b Z. If 3 ab then 31(a + b). b. Let n, k, l € Z. If n+k+1 = 101 then two of these integers have opposite parity. c. Let n € Z. If 3|n and 2 n then there exists k € Z such that n = 6k+3. FRI

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 10TFE

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