Why isn't the answer to TMUA-P2-ARG4-012 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ARG4-012 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ARG4-012?

No — calculators are banned in the TMUA. TMUA-P2-ARG4-012 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ARG4-012?

TMUA-P2-ARG4-012 is Paper P2 · Negation (specification code ARG4), level 1. Drill more of the same topic from this page.

TMUA-P2-ARG4-012 — Paper P2 · Negation · Level 1

P2ARG4Level 1~150s target

Spec: ARG4 · No calculator · ~150s

What is the negation of “If it rains then the match is cancelled”?

Options

It rains and the match is not cancelled.
If it does not rain then the match is not cancelled.
If the match is not cancelled then it did not rain.
It does not rain or the match is cancelled.

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: implication-negation, converse-vs-contrapositive. Name the trap first, work the stem by hand, then open the solution below.

Show solution

\lnot(P \Rightarrow Q)

P \land \lnot Q

: the hypothesis holds but the conclusion fails. Trap: the inverse (“If not

P

then not

Q

”) and the contrapositive look similar but are not negations; the last option restates the implication.

Keep practising

Same topic · same level
P2ARG4Level 1
TMUA-P2-ARG4-001
Let P and Q be statements. Which of the following is the negation of “ P and Q ”?
Negation
Open TMUA-P2-ARG4-001 →
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 →
Step up a level
P2ARG4Level 2
TMUA-P2-ARG4-004
Consider the claim “Every prime number greater than 2 is odd”. Which of the following is its negation?
Negation
Open TMUA-P2-ARG4-004 →

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Keep practising

Same topic · same level

P2ARG4Level 1

TMUA-P2-ARG4-001

Let P and Q be statements. Which of the following is the negation of “ P and Q ”?

Negation

Open TMUA-P2-ARG4-001 →

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 →

Step up a level

P2ARG4Level 2

TMUA-P2-ARG4-004

Consider the claim “Every prime number greater than 2 is odd”. Which of the following is its negation?

Negation

Open TMUA-P2-ARG4-004 →

TMUA-P2-ARG4-012 — Paper P2 · Negation · Level 1

Options

Keep practising

Master Negation

TMUA-P2-ARG4-012 — Paper P2 · Negation · Level 1

Options

Keep practising

Master Negation