1

### 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

2

### 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".
3

### JEE Main 2018 (Offline)

The Boolean expression

$\sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$ is equvalent to
A
${ \sim q}$
B
${ \sim p}$
C
p
D
q

## Explanation

From the table you can see ~p and
~(p $\vee$ q) $\vee$ (~p $\wedge$ q) are equivalent.
4

### JEE Main 2018 (Online) 15th April Morning Slot

If (p $\wedge$ $\sim$ q) $\wedge$ (p $\wedge$ r) $\to$ $\sim$ p $\vee$ q is false, then the truth values of $p, q$ and $r$ are, respectively :
A
F, T, F
B
T, F, T
C
T, T, T
D
F, F, F

## Explanation

From the truth table you can see (p $\wedge$ ~q) $\wedge$ (p $\wedge$ r) $\to$ ~p $\vee$ q is false only when values of (p, q, r) is (T, F, T).