1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number if and only if y is a transcendental number”. Statement-1 : r is equivalent to either q or p Statememt-2 : r is equivalent to (p↔∼q)

A
Statement – 1 is false, Statement – 2 is true
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement -1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement -1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

Statement – 1 is true. Statement – 2 is false

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A Statement – 1 is false, Statement – 2 is truep : x is an irrational number q : y is a transcendental number r : x is a rational number iff y is a transcendental number. Clearly r: ∼p↔q Let us use truth table to check the equivalence of 'r' and 'q or p'; 'r' and (p↔∼q) 12 3pq∼p∼q∼p↔qq or pp↔∼q∼(p↔∼q)TTFFFTFTTFFTTTTFFTTFTTTFFFTTFFFT From columns (1) and (2), we observe, r≡(p↔∼q) ∴ Statement-1 is false and statement-2 is true. Option (a) is correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Validity of Statements
MATHEMATICS
Watch in App
Join BYJU'S Learning Program