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7. Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is a multiple of 6. (a) Prove the statement. What sort of proof are you using? (b) State the converse. Is it true? Prove or disprove.

7. Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is a multiple of 6. (a) Prove the statement. What sort of proof are you using? (b) State the converse. Is it true? Prove or disprove.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 44E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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7. Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is a multiple of 6. (a) Prove the statement. What sort of proof are you using? (b) State the converse. Is it true? Prove or disprove.
Transcribed Image Text:7. Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is a multiple of 6. (a) Prove the statement. What sort of proof are you using? (b) State the converse. Is it true? Prove or disprove.
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