1

### 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 2

### 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
3

### 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)

## Explanation

It is obvious
4

### JEE Main 2019 (Online) 11th January Morning Slot

If q is false and p $\wedge$ q $\leftrightarrow$ r is true, then which one of the following statements is a tautology ?
A
P $\wedge$ r
B
(p $\vee$ r) $\to$ (p $\wedge$ r)
C
p $\vee$ r
D
(p $\wedge$ r) $\to$ (p $\vee$ r)

## Explanation

Given q is F and (p $\wedge$ q) $\leftrightarrow$ r is T

$\Rightarrow$  p $\wedge$ q is F which implies that r is F

$\Rightarrow$  q is F and r is F

$\Rightarrow$  (p $\wedge$ r) is always F

$\Rightarrow$  (p $\wedge$ r) $\to$ (p $\vee$ r) is tautology.