Consider the following statement, for all x E Z: If x + 1 is even, then 3x² - 4 is odd. The correct way to start a direct proof to determine if the statement is true is as follows: Assume x is even, then x = 2k for some k € Z, then 3x²-4 ie 3(2k)2-4 i.e. a. True b. False

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following statement, for all x E Z:
If x + 1 is even, then 3x² - 4 is odd.
The correct way to start a direct proof to determine if the statement is true is as follows:
Assume x is even, then x = 2k for some k € Z, then
3x²4 ie 3(2k)2 - 4 i.e...........
a. True
b. False
Transcribed Image Text:Consider the following statement, for all x E Z: If x + 1 is even, then 3x² - 4 is odd. The correct way to start a direct proof to determine if the statement is true is as follows: Assume x is even, then x = 2k for some k € Z, then 3x²4 ie 3(2k)2 - 4 i.e........... a. True b. False
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