Question bank

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?

TMUA-P2-ARG1-002

In mathematics “$P$ or $Q$” uses the inclusive or. The statement “$P$ or $Q$” is FALSE in exactly which case?

TMUA-P2-ARG1-003

Consider the statement “If $n$ is even then $n^2$ is even”, where $n$ is an integer. Which of the following is its contr…

TMUA-P2-ARG1-004

Let $P$ and $Q$ be statements. The claim “$P$ if and only if $Q$” (written $P \iff Q$) asserts which of the following?

TMUA-P2-ARG1-005

Let $P$ and $Q$ be statements. The conditional “If $P$ then $Q$” is FALSE in exactly which circumstance?

TMUA-P2-ARG1-006

A school debating society announces the following rule for its committee election: every student who voted for motion $A…

TMUA-P2-ARG1-007

The notice reads: “A number $n$ is prime greater than $2$ only if $n$ is odd.” If $P$ is “$n$ is prime greater than $2$”…

TMUA-P2-ARG1-008

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

TMUA-P2-ARG1-009

A textbook exercise states the following facts about positive integers, where $P$ is “$n$ is divisible by $6$” and $Q$ i…

TMUA-P2-ARG1-010

The sports department publishes this registration rule for its two lunchtime clubs: a pupil may join the chess club only…

TMUA-P2-ARG1-011

The statement “If it rains, then the match is cancelled” is logically equivalent to which of the following?

TMUA-P2-ARG1-012

Let $P$ be “$n$ is divisible by $12$” and $Q$ be “$n$ is divisible by $4$”, where $n$ is a positive integer. The convers…

TMUA-P2-ARG1-013

A poster states: “An integer $n$ is a perfect cube only if $n^2$ is a perfect cube.” Let $P$ be “$n$ is a perfect cube”…

TMUA-P2-ARG1-014

Consider the statement “If $x > 0$ then $x^2 > 0$”, where $x$ is real. Which of the following is its inverse?

TMUA-P2-ARG1-015

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

TMUA-P2-ARG1-016

A library notice reads: every pupil who borrowed the star atlas also reserved a reading seat. Later it is found that The…

TMUA-P2-ARG1-017

Let $P$ be “a quadrilateral is a square” and $Q$ be “it has four equal sides”. The original implication “If $P$ then $Q$…

TMUA-P2-ARG1-018

A leisure centre states: members may book the squash court only if they have completed an induction, and the coach adds…