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Prove directly if the statements that are true, give counterexamples to disprove those that are false. (1). V m, n E Z, ifm mod 6 = 5 and n mod 6 = 2 then mn mod 6 = 4. 2. (2). V m, n ɛ Z, if m | n³ and m Sn then m | n.

Prove directly if the statements that are true, give counterexamples to disprove those that are false. (1). V m, n E Z, ifm mod 6 = 5 and n mod 6 = 2 then mn mod 6 = 4. 2. (2). V m, n ɛ Z, if m | n³ and m Sn then m | n.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 29E: 29. Find the least positive integer that is congruent to the given sum, product, or power. a. ...
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2. Prove directly if the statements that are true, give counterexamples to disprove those that are false. (1). V m, n e Z, ifm mod 6 = 5 and n mod 6 = 2 then mn mod 6 = 4. (2). V m, n e Z, if m | n3 and m <n then m | n.
Transcribed Image Text:2. Prove directly if the statements that are true, give counterexamples to disprove those that are false. (1). V m, n e Z, ifm mod 6 = 5 and n mod 6 = 2 then mn mod 6 = 4. (2). V m, n e Z, if m | n3 and m <n then m | n.
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