Why isn't the answer to TMUA-P2-ARG1-017 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ARG1-017 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ARG1-017?

No — calculators are banned in the TMUA. TMUA-P2-ARG1-017 is set for a no-calculator target of about 260 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ARG1-017?

TMUA-P2-ARG1-017 is Paper P2 · Statements and connectives (specification code ARG1), level 3. Drill more of the same topic from this page.

TMUA-P2-ARG1-017 — Paper P2 · Statements and connectives · Level 3

P2ARG1Level 3~260s target

Spec: ARG1 · No calculator · ~260s

Let

P

be “a quadrilateral is a square” and

Q

be “it has four equal sides”. The original implication “If

P

then

Q

” is true. A rhombus that is not a square (four equal sides, angles

60^\circ

and

120^\circ

) exists. Which student describes the converse, inverse and contrapositive correctly, including truth values?

Options

Converse true, inverse true, contrapositive false.
All three of converse, inverse and contrapositive are true.
Converse false (the non-square rhombus), inverse false (the same rhombus), contrapositive true.
Converse false, inverse true, contrapositive true.

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: converse-vs-contrapositive, single-counterexample. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Original

P \Rightarrow Q

is true, so its contrapositive is true. The converse “If four equal sides then a square” is refuted by the non-square rhombus; the inverse “If not a square then not four equal sides” is refuted by the same rhombus. Trap: assuming converse and inverse inherit truth from the original — only the contrapositive does.

Keep practising

Same topic · same level
P2ARG1Level 3
TMUA-P2-ARG1-009
A textbook exercise states the following facts about positive integers, where P is “ n is divisible by 6 ” and Q is “ n…
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Same trap: converse-vs-contrapositive
P2ARG1Level 1
TMUA-P2-ARG1-001
Let P and Q be mathematical statements. The converse of the statement “If P then Q ” is which of the following?
Statements and connectives
Open TMUA-P2-ARG1-001 →
More in this topic
P2ARG1Level 3
TMUA-P2-ARG1-010
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Browse more

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Options

Converse true, inverse true, contrapositive false.

All three of converse, inverse and contrapositive are true.

Converse false (the non-square rhombus), inverse false (the same rhombus), contrapositive true.

Converse false, inverse true, contrapositive true.

Letters only — the answer key is hidden. Work it out, then check the solution below.

Keep practising

Same topic · same level

P2ARG1Level 3

TMUA-P2-ARG1-009

A textbook exercise states the following facts about positive integers, where P is “ n is divisible by 6 ” and Q is “ n…

Statements and connectives

Open TMUA-P2-ARG1-009 →

Same trap: converse-vs-contrapositive

P2ARG1Level 1

TMUA-P2-ARG1-001

Let P and Q be mathematical statements. The converse of the statement “If P then Q ” is which of the following?

Statements and connectives

Open TMUA-P2-ARG1-001 →

TMUA-P2-ARG1-017 — Paper P2 · Statements and connectives · Level 3

Options

Keep practising

Master Statements and connectives

TMUA-P2-ARG1-017 — Paper P2 · Statements and connectives · Level 3

Options

Keep practising

Master Statements and connectives