Question bank

TMUA-P2-ARG3-001

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

TMUA-P2-ARG3-002

What does the statement “There exists an integer $n$ such that $n^3 = 8$” assert?

TMUA-P2-ARG3-003

Consider (S1) “For every integer $x$ there is an integer $y$ with $y > x$” and (S2) “There is an integer $y$ such that f…

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?

TMUA-P2-ARG3-005

Consider the statement “For every real number $x$ there exists an integer $n$ with $n > x$”. Which of the following is c…

TMUA-P2-ARG3-006

A teacher announces to a class of thirty pupils: “For every pupil $s$ there is a project title $t$ on the list such that…

TMUA-P2-ARG3-007

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

TMUA-P2-ARG3-008

What is the logical negation of the statement “For every real number $x$, $x^2 \ge 0$”?

TMUA-P2-ARG3-009

Consider $A$: “For every real $x$ there is a real $y$ with $y > x$” and $B$: “There is a real $y$ such that for every re…

TMUA-P2-ARG3-010

A student claims: “For every integer $n$, $n^2+n+41$ is prime.” Which single observation disproves it?

TMUA-P2-ARG3-011

Let $P(m,n)$ be “$m+n=n$” for integers. What is the negation of “There exists an integer $m$ such that for every integer…

TMUA-P2-ARG3-012

The sentence “Every multiple of $6$ is a multiple of $3$” is logically equivalent to which conditional?

TMUA-P2-ARG3-013

Which formula correctly expresses “There is no integer that is both even and odd”?

TMUA-P2-ARG3-014

Let $U$ be “$\forall x\,\exists y\,(y > x)$” and $V$ be “$\exists y\,\forall x\,(y > x)$” over $\mathbb{R}$. Which is co…

TMUA-P2-ARG3-015

What is the negation of “For every real $x$ there is a real $y$ such that for every real $z$, $xyz=0$”?

TMUA-P2Y-ARG-001

What does the statement “For every integer $m$, the number $m^2 - m$ is even” assert?

TMUA-P2Y-ARG-002

Consider the statement “There exists an integer $k$ such that $k^2 = 64$”. What does it assert, and is it true?

TMUA-P2Y-ARG-003

Consider (A) “For every integer $a$ there is an integer $b$ with $b = a^2$” and (B) “There is an integer $b$ such that f…

TMUA-P2Y-ARG-004

Consider the claim “For every integer $n$, the product $n(n+1)$ is even”. Which of the following is correct?

TMUA-P2Y-ARG-005

A tutor writes two statements about divisibility, where $d$ and $M$ denote integers: (T1) “For every integer $d \ne 0$ t…

TMUA-P2Y-ARG-006

A worksheet asks pupils to compare two claims, where all letters denote integers: claim one says “There exists a nonzero…