Question bank

TMUA-P2-PRF4-001

The claim “Every prime $p$ is odd” is universal. Which single observation disproves it?

TMUA-P2-PRF4-002

Disprove the claim: “For all positive integers $a, b, c$, if $a \mid bc$ then $a \mid b$ or $a \mid c$.”

TMUA-P2-PRF4-003

Disprove the claim: “For every real number $x$, $|x| > x$.”

TMUA-P2-PRF4-004

Disprove the claim: “For all angles $A$ and $B$ with $0^\circ \le A, B \le 180^\circ$, if $\sin A = \sin B$ then $A = B$…

TMUA-P2-PRF4-005

A student conjectures: “For every non-negative integer $n$, the number $n^2 + n + 41$ is prime.” The first values $n = 0…

TMUA-P2-PRF4-006

Disprove the claim: “For every real number $x$, $x^2 > x$.”

TMUA-P2-PRF4-007

An olympiad-style training sheet invites students to test the sweeping divisibility conjecture that for all integers $m$…

TMUA-P2Y-PRF-011

Disprove the universal claim: for every integer $n \ge 0$, the number $2n + 1$ is prime.

TMUA-P2Y-PRF-012

Disprove the claim: for all real numbers $x$ and $y$, $(x + y)^2 = x^2 + y^2$.

TMUA-P2Y-PRF-013

Disprove the claim: for all integers $a$ and $b$, if $a^2 = b^2$ then $a = b$.