Embibe Experts Solutions for Chapter: Mathematical Reasoning, Exercise 2: Exercise-2

Let $p$ and $q$ be any two propositions.

Statement $1:\left(p\to q\right)\leftrightarrow q\vee ~p$ is a tautology.
Statement $2:~\left(~p\wedge q\right)\wedge \left(p\vee q\right)\leftrightarrow p$ is a fallacy.

Statement-$1:$Consider the statements

$p:$ Sachin Tendulakar is a good cricketer.
$q:$ Mukesh Ambani is a rich person in india.

Then the negation of statement $p\vee q$, is 'Sachin Tendulakar is not a good cricketer and Mukesh Ambani is not a rich person in india".

Statement-$2:$ For any two statements $p$ and $q$, $~\left(p\vee q\right)=~p\vee ~q$.

Statement-$1: ~(p\leftrightarrow ~q)$ is equivalent to $p\leftrightarrow q.$

Statement-$2: ~(p\leftrightarrow ~q)$ is a tautology.

Statement-$1:$ The type of $"\mathrm{OR}"$ used in the statement "You may have a voter card or a PAN card for your identity proof" is inclusive $\mathrm{OR}$.

Statement-$2:$ Inclusive $\mathrm{OR}$ is said to be used in a statement if its component statements both may happen together.

Which of the following statements is using an "exclusive Or" ?

In which of the following compound statements, the connective "or" is exclusive?

Which of the following is a fallacy?

Statement $p:$ "An equilateral triangle is equiangular" then negation of statement $p$ is