X2 - Proof

What is the negation of the statement:

If a triangle has two equal sides, then it has two equal angles.

• If a triangle does not have two equal sides, then it does not have two equal angles.

• If a triangle does not have two equal angles, then it does not have two equal sides.

• A triangle has two equal sides and it does not have two equal angles.

• A triangle has two equal angles and it does not have two equal sides.

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Answer explanation

From 2022 HSC paper

Tags

2022 HSC

Answer explanation

From 2022 HSC paper

• The statement P and its converse are both true.

• The statement P and its converse are both false.

• The statement P is true and its converse is false.

• The statement P is false and its converse is true.

Answer explanation

From 2022 HSC paper

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?

• There exists an integer n such that n is a multiple of 6 and not a multiple of 2.

• There exists an integer n such that n is a multiple of 2 and not a multiple of 6.

• For all integers n, if n is not a multiple of 2, then n is not a multiple of 6.

• For all integers n, if n is not a multiple of 6, then n is not a multiple of 2.

Answer explanation

From 2021 HSC paper

Which of the following statements is FALSE?

Answer explanation

From 2021 HSC

Answer explanation

From 2020 HSC paper.

Consider the statement:

‘If n is even, then if n is a multiple of 3, then n is a multiple of 6’.

Which of the following is the negation of this statement?

• n is odd and n is not a multiple of 3 or 6.

• n is even and n is a multiple of 3 but not a multiple of 6.

• If n is even, then n is not a multiple of 3 and n is not a multiple of 6.

• If n is odd, then if n is not a multiple of 3 then n is not a multiple of 6.

Answer explanation

2020 HSC Q8

Answer explanation

Answer explanation