Skip to main content

Back to the full dot-point answer

VICSpecialist MathematicsQuick questions

Unit 3: Algebra, number and structure

Quick questions on Proof methods and counterexamples: VCE Specialist Mathematics Unit 3

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is choose the contrapositive?
Show answer
The direct route would require deducing the parity of nn from n2n^2, which is indirect. The contrapositive of "n2n^2 odd ⇒\Rightarrow nn odd" is "nn even ⇒\Rightarrow n2n^2 even", which is straightforward.
What is prove the contrapositive?
Show answer
Suppose nn is even, so n=2kn = 2k for some integer kk. Then
What is conclude?
Show answer
We have shown "nn even ⇒\Rightarrow n2n^2 even". This is the contrapositive of the original statement and is logically equivalent to it, so "if n2n^2 is odd then nn is odd" is proved.
What is q1?
Show answer
State the contrapositive of "if it rains then the ground is wet". [1 mark]
What is q2?
Show answer
Disprove "every multiple of 33 is odd". [1 mark]
What is q3?
Show answer
Outline a proof by contradiction that there is no largest integer. [2 marks]

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All Specialist MathematicsQ&A pages