JEE Exam  >  JEE Questions  >  Let a: (p ∧ - r) ∨ (-q ∨ s) and b: ... Start Learning for Free
Let a: (p - r) (-q s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...

  • a)
    T, F

  • b)
    T, T

  • c)
    F, F

  • d)
    F, T

Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q &an...
Let's break down the truth values of a and b using the given truth values of p, q, r, and s.



Given: p = true, q = true, r = false, s = false.



a: (p ∧ - r) ∨ (-q ∨ s)

a: (true ∧ - false) ∨ (-true ∨ false)

a: (true ∧ true) ∨ (false ∨ false)

a: true ∨ false

a: true



b: (p ∨ s) ↔ (-q ∧ r)

b: (true ∨ false) ↔ (-true ∧ false)

b: true ↔ (false ∧ false)

b: true ↔ false

b: false



So, the truth values of a and b are True and False, respectively. The correct answer is:



T, F
Free Test
Community Answer
Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q &an...
Truth Values of Propositions a and b

Given propositions a and b:
a: - (p ∧ - r) ∨ (-q ∨ s)
b: (p ∨ s) ↔ (-q ∧ r)

Truth values of p, q, r, and s are:
p = T (true)
q = T (true)
r = F (false)
s = F (false)

Using these truth values, we can evaluate the truth values of propositions a and b.

Truth value of proposition a:

a = - (p ∧ - r) ∨ (-q ∨ s)
= - (T ∧ - F) ∨ (-T ∨ F) (substituting truth values of p, q, r, and s)
= - T ∨ -T (evaluating the first part of the expression)
= F (evaluating the second part of the expression)

Therefore, the truth value of proposition a is F (false).

Truth value of proposition b:

b = (p ∨ s) ↔ (-q ∧ r)
= (T ∨ F) ↔ (-T ∧ F) (substituting truth values of p, q, r, and s)
= T ↔ F (evaluating the first part of the expression)
= F (evaluating the second part of the expression)

Therefore, the truth value of proposition b is F (false).

Conclusion:

The truth values of propositions a and b are F (false) when p = T, q = T, r = F, and s = F. The correct answer is option A.
Explore Courses for JEE exam
Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer?
Question Description
Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let a: (p ∧ - r) ∨ (-q ∨ s) and b: (p ∨ s) ↔ (-q ∧ r). If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are, respectively...a)T, Fb)T, Tc)F, Fd)F, TCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev