1

### JEE Main 2016 (Online) 10th April Morning Slot

The contrapositive of the following statement,

“If the side of a square doubles, then its area increases four times”, is :
A
If the side of a square is not doubled, then its area does not increase four times.
B
If the area of a square increases four times, then its side is doubled.
C
If the area of a square increases four times, then its side is not doubled.
D
If the area of a square does not increase four times, then its side is not doubled.

## Explanation

Contrapositive of p $\to$ q is $\sim$q $\to$ $\sim$p.

Here,

Let

p = Side of a square is doubles.

q = Area of square increases four times.

$\therefore$   $\sim$q $\to$ $\sim$p = If the area of a square does not increase four times, then its side is not doubled.
2

### JEE Main 2017 (Offline)

The following statement

$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$ is
A
equivalent to ${ \sim p \to q}$
B
equivalent to ${p \to \sim q}$
C
a fallacy
D
a tautology

## Explanation

We have

p q ~p p$\to$q ~p$\to$q (~p$\to$q)$\to$q (p$\to$q)$\to$((~p$\to$q)$\to$q)
T F F F T F T
T T F T T T T
F F T T F T T
F T T T T T T

$\therefore$ It is tautology.
3

### JEE Main 2017 (Online) 8th April Morning Slot

The proposition $\left( { \sim p} \right) \vee \left( {p \wedge \sim q} \right)$ is equivalent to :
A
p $\vee$ ~ q
B
p $\to$ ~ q
C
p $\wedge$ ~ q
D
q $\to$ p

## Explanation 4

### JEE Main 2017 (Online) 9th April Morning Slot

Contrapositive of the statement

‘If two numbers are not equal, then their squares are not equal’, is :
A
If the squares of two numbers are equal, then the numbers are equal.
B
If the squares of two numbers are equal, then the numbers are not equal.
C
If the squares of two numbers are not equal, then the numbers are not equal.
D
If the squares of two numbers are not equal, then the numbers are equal.

## Explanation

Let,

p : two numbers are not equal

q : squares of two numbers are not equal

Contrapositive of p $\to$ q is $\sim$q $\to$ $\sim$p.

$\therefore$ $\sim$q $\to$ $\sim$p means "If the squares of two numbers are equal, then the numbers are equal".