1

### 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 = $\left( { \wedge , \vee } \right)$
2

### 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

3

### 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
4

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

Consider the following three statements :

P : 5 is a prime number

Q : 7 is a factor of 192

R : L.C.M. of 5 and 7 is 35

Then the truth value of which one of the following statements is true ?
A
(P $\wedge$ Q) $\vee$ ($\sim$ R)
B
P $\vee$ ($\sim$ Q $\wedge$ R)
C
(~ P) $\wedge$ ($\sim$ Q $\wedge$ R)
D
($\sim$ P) $\vee$ (Q $\wedge$ R)

It is obvious