1

### JEE Main 2018 (Online) 16th April Morning Slot

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

## Explanation

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

From the truth table,

p $\to$ (~p $\vee$ ~q) is false only when p and q both are true.
2

### JEE Main 2019 (Online) 9th January Morning Slot

If the Boolean expression
(p $\oplus$ q) $\wedge$ (~ p $\odot$ q) is equivalent
to p $\wedge$ q, where $\oplus , \odot \in \left\{ { \wedge , \vee } \right\}$, then the
ordered pair $\left( { \oplus , \odot } \right)$ is :
A
$\left( { \vee , \wedge } \right)$
B
$\left( { \vee , \vee } \right)$
C
$\left( { \wedge , \vee } \right)$
D
$\left( { \wedge , \wedge } \right)$

## Explanation

Given that, (p $\oplus$ q) $\wedge$ (~ p $\odot$ q) $\equiv$ p $\wedge$ q.

From the truth table you can see this equivalence only hold when ordered pair $\left( { \oplus , \odot } \right)$ is = $\left( { \wedge , \vee } \right)$
3

### JEE Main 2019 (Online) 9th January Evening Slot

The logical statement

[ $\sim$ ( $\sim$ p $\vee$ q) $\vee$ (p $\wedge$ r)] $\wedge$ ($\sim$ q $\wedge$ r) is equivalent to :
A
( $\sim$ p $\wedge$ $\sim$ q) $\wedge$ r
B
$\sim$ p $\vee$ r
C
(p $\wedge$ r) $\wedge$ $\sim$ q
D
(p $\wedge$ $\sim$ q) $\vee$ r

## Explanation

4

### JEE Main 2019 (Online) 10th January Morning Slot

Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ?
A
P(5) is false but P(3) is true
B
Both P(3) and P(5) are true
C
P(3) is false but P(5) is true
D
Both P(3) and P(5) are false

## Explanation

P(n) : n2 $-$ n + 41 is prime

P(5) = 61 which is prime

P(3) = 47 which is also prime