Consider the statement:
‘For all integers n, if n is a multiple of 6, then n is a multiple of 2’ - HSC - SSCE Mathematics Extension 2 - Question 4 - 2021 - Paper 1
Question 4
Consider the statement:
‘For all integers n, if n is a multiple of 6, then n is a multiple of 2’.
Which of the following is the contrapositive of the statement?
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Worked Solution & Example Answer:Consider the statement:
‘For all integers n, if n is a multiple of 6, then n is a multiple of 2’ - HSC - SSCE Mathematics Extension 2 - Question 4 - 2021 - Paper 1
Step 1
Identify the Original Statement
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Answer
The original statement is: ‘For all integers n, if n is a multiple of 6, then n is a multiple of 2’.
Step 2
Formulate the Contrapositive
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Answer
The contrapositive of a statement of the form ‘if P then Q’ is ‘if not Q then not P’. In this case:
Let P: n is a multiple of 6
Let Q: n is a multiple of 2
Thus, the contrapositive is: ‘For all integers n, if n is not a multiple of 2, then n is not a multiple of 6’.
Step 3
Select the Correct Option
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Answer
The correct answer is C: For all integers n, if n is not a multiple of 2, then n is not a multiple of 6.
