Solution to Question 24 Consider the statement If n is a multiple of 3, then 2n + … - Sikademy
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Archangel Macsika

Question 24 Consider the statement If n is a multiple of 3, then 2n + 2 is not a multiple of 3. The converse of the given statement is: If n is not a multiple of 3, then 2n + 2 is a multiple of 3. 1. True 2. False Question 25 Consider the following statement, for all x  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 ie ……….. 1. True 2. False

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Question 24


Consider the statement "If n is a multiple of 3, then 2n + 2 is not a multiple of 3". The converse of a statement is formed by switching the hypothesis and the conclusion. Hence, the converse of the given statement is "If 2+2n is not a multiple of 3, then n is a multiple of 3".


Answer: 2. False



Question 25


Consider the following statement, "for all x \in\Z : If x + 1 is even, then 3x^2- 4 is odd. 

The correct way to start a direct proof to determine if the statement is true is as follows:

 Assume x+1 is even, then x +1= 2k for some k \in \Z,  then 3x^2 – 4=3(2k-1)^2 – 4 ...


Answer: 2. False

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