Why isn't the answer to TMUA-P2-ARG3-003 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ARG3-003 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ARG3-003?

No — calculators are banned in the TMUA. TMUA-P2-ARG3-003 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ARG3-003?

TMUA-P2-ARG3-003 is Paper P2 · Quantifiers (specification code ARG3), level 2. Drill more of the same topic from this page.

TMUA-P2-ARG3-003 — Paper P2 · Quantifiers · Level 2

P2ARG3Level 2~210s target

Spec: ARG3 · No calculator · ~210s

Consider (S1) “For every integer

x

there is an integer

y

with

y > x

” and (S2) “There is an integer

y

such that for every integer

x

y > x

”. Which evaluation is correct?

Options

Both S1 and S2 are true.
Both S1 and S2 are false.
S1 is true (given $x$ , take $y = x + 1$ ) but S2 is false (no greatest integer exists).
S1 is false but S2 is true.
S1 and S2 mean the same thing.

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: quantifier-negation-flip. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Order matters: S1 lets

y

depend on

x

(true via

y = x+1

), while S2 demands one

y

bigger than every integer (impossible). Trap: treating the quantifiers as commuting — swapping

\forall

and

\exists

changes the meaning.

Keep practising

Same topic · same level
P2ARG3Level 2
TMUA-P2-ARG3-004
The sentence “For some prime p, p is even” is a quantified claim about primes. What does it mean, and is it true?
Quantifiers
Open TMUA-P2-ARG3-004 →
Same trap: quantifier-negation-flip
P2ARG3Level 1
TMUA-P2-ARG3-001
What does the statement “For all integers n, n^2 0 ” assert?
Quantifiers
Open TMUA-P2-ARG3-001 →
Step up a level
P2ARG3Level 3
TMUA-P2-ARG3-007
A number-theory worksheet asks pupils to compare two claims about even sums, where all letters denote integers: claim on…
Quantifiers
Open TMUA-P2-ARG3-007 →

Browse more

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Keep practising

Same topic · same level

P2ARG3Level 2

TMUA-P2-ARG3-004

The sentence “For some prime p, p is even” is a quantified claim about primes. What does it mean, and is it true?

Quantifiers

Open TMUA-P2-ARG3-004 →

Same trap: quantifier-negation-flip

P2ARG3Level 1

TMUA-P2-ARG3-001

What does the statement “For all integers n, n^2 0 ” assert?

Quantifiers

Open TMUA-P2-ARG3-001 →

Step up a level

P2ARG3Level 3

TMUA-P2-ARG3-007

A number-theory worksheet asks pupils to compare two claims about even sums, where all letters denote integers: claim on…

Quantifiers

Open TMUA-P2-ARG3-007 →

TMUA-P2-ARG3-003 — Paper P2 · Quantifiers · Level 2

Options

Keep practising

Master Quantifiers

TMUA-P2-ARG3-003 — Paper P2 · Quantifiers · Level 2

Options

Keep practising

Master Quantifiers