Question bank

TMUA-P2-ARG4-001

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

TMUA-P2-ARG4-002

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

TMUA-P2-ARG4-003

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

TMUA-P2-ARG4-004

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

TMUA-P2-ARG4-005

Consider the statement “There exists a real number $x$ with $x^2 = 2$”. Which of the following is its negation?

TMUA-P2-ARG4-006

A headteacher announces at assembly that every pupil who submitted the holiday homework passed the September test, and t…

TMUA-P2-ARG4-007

Let $x$ be a real number. Which of the following is the negation of “$x > 2$ and $x < 5$”?

TMUA-P2-ARG4-008

During a fire drill debrief, the safety officer states the following evacuation rule with $P$ = “the alarm rings” and $Q…

TMUA-P2-ARG4-009

A stretch-and-challenge sheet makes the ambitious claim that for every integer $n$ there exists an integer $m$ such that…

TMUA-P2-ARG4-010

An analysis primer states the familiar property of non-negative reals in fully quantified form: for every real number $x…

TMUA-P2-ARG4-011

What is the negation of “$n$ is even and $n$ is a multiple of $3$”?

TMUA-P2-ARG4-012

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

TMUA-P2-ARG4-013

What is the negation of “$x > 2$ or $x < -2$” (i.e. $|x| > 2$)?

TMUA-P2-ARG4-014

“Neither $P$ nor $Q$” is logically equivalent to which of the following?

TMUA-P2-ARG4-015

What is the negation of “$x$ is positive and ($y$ is positive or $z$ is positive)”?

TMUA-P2-ARG4-016

“It is false that $n$ is neither prime nor odd.” What does this mean?

TMUA-P2-ARG4-017

What is the negation of “If $P$ then ($Q$ or $R$)”?

TMUA-P2-ARG4-018

What is the negation of “Either ($x>0$ and $y>0$) or $z \le 0$”?

TMUA-P2-ARG4-019

What is the negation of “For every integer $n$, $n$ is even and $n^2$ is even”?