Mathematical Reasoning * — JEE Main PYQs

The negation of $\sim \mathrm{s}\vee (\sim \mathrm{r}\wedge \mathrm{s})$ is equivalent to :

The statement $\sim (p\leftrightarrow \sim q)$ is

Consider :

Statement - I: $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.

Statement - II : $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

The negation of the statement "If I become a teacher, then I will open a school" is

Consider the following statements

P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

Let S be a non-empty subset of R. Consider the following statement:
$P$ : There is a rational number $x\in S$ such that $x>0$.
Which of the following statements is the negation of the statement $P$ ?

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

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

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and $r$ be the statement "$x$ is a rational number iff $y$ is a transcendental number".
Statement $-1:r$ is equivalent to either $q$ or $p$
Statement -2 : $r$ is equivalent to …

The statement $p\to (q\to p)$ is equivalent to