JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 1 - MCQExams.com

If p is the statement 'Ravi races' and q is the statement `Ravi wins'. Then, the verbal translation of ~ [p ⋁ (~ q)] is
  • Ravi does not race and Ravi does not win
  • It is not true that Ravi races and that Ravi does not win
  • Ravi does not race and Ravi wins
  • It is not true that Ravi does not race or that Ravi does not win
  • It is not that Ravi does not race and Ravi does not win
The negation of the proposition `If 2 is prime, then 3 is odd' is
  • if 2 is not prime, then 3 is not odd
  • 2 is prime and 3 is not odd
  • 2 is not prime and 3 is odd
  • if 2 is not prime, then 3 is odd
If p ⇒(q ˅ r) is false, then the truth values of p, q, r arerespectively
  • T, F, F
  • F, F, F
  • F, T, T
  • T, T, F
The logically equivalent proposition of p ⇔ q is
  • (p ˄q) ˅(p ˄ q)
  • (p⇒ q) ˄ (q⇒ p)
  • (p ˄q) ˅ (q⇒ p)
  • (p ˄q)⇒ (q ˅ p)
The false statement in the following is
  • p ˄ (~p) is a contradiction
  • (p ⇒ q) ⇔ (~q⇒~p) is a contradiction
  • ~ (~p) ⇔ p is a tautology
  • p ˅ (~ p) ⇔ is a tautology
~(p ⋁ q ) ⋁ (~ p ⋀ q) is logically equivalent to
  • ~q
  • ~ p
  • p
  • q
The contrapositive of (p ⋁ q) → r is
  • ~ r → (p ⋁ q)
  • r → (p ⋁ q)
  • ~ r → (~ p ⋀ ~ q)
  • p → (q ⋁ r)
Negation of the conditional, 'If it rains, I shall go to school' is
  • It rains and I shall go to school
  • It rains and I shall not go to school
  • It does not rains and I shall go to school
  • None of the above
Dual of (x' ⋁ y')' = x ⋀ y is
  • (x' ⋁ y') = x ⋁ y
  • (x' ⋀ y')' = x ⋁ y
  • (x' ⋀ y') = x ⋀ y
  • None of these
The converse of the contrapositive of the conditional p → ~q is
  • p → q
  • ~ p → ~ q
  • ~ q → p
  • ~ p → q

Maths-Mathematical Logic and Boolean Algebra-38003.png
  • tautology
  • contradiction
  • Neither tautology nor contradiction
  • Either tautology nor contradiction
Which of the following is not a correct statement ?
  • Mathematics is interesting
  • √3 is a prime number
  • √2 is irrational number
  • The sun is a star
If S be a non-empty subset of R.
Consider the following statement
P : There is a rational number x ϵ S such that x > 0.
Which of the following statements is the negation of the statement P ?
  • There is a rational number x ϵ S such that x ≤ 0
  • There is no rational number x ϵ S such that x ≤ 0
  • Every rational number x ϵ S satisfies x ≤ 0
  • x ϵ S and x ≤ 0 ⇒ x is not rational
Which of the following Statements is a tautology ?
  • (~ q ⋀ p) ⋀ q
  • (~ q ⋀ p) ⋀ (p ⋀ ~ p)
  • (~q ⋀ p) ⋁ (p ⋁ ~ q)
  • (p ⋀ q) ⋀ [~ (p ⋀ q)]
Simplify the following circuit and find the boolean polynomial
Maths-Mathematical Logic and Boolean Algebra-38004.png
  • p ⋁ (q ⋀ r)
  • p ⋀ (q ⋁ r)
  • p ⋁ (q ⋁ r)
  • p ⋀ (q ⋀ r)
Negation of 'Paris is in France and London is in England' is
  • Paris is in England and London is in France
  • Paris is not in France or London is not in England
  • Paris is in England or London is in France
  • None of the above
If p, q and rare simple propositions with truth values T, F, T, then the truth value of [(~ p ⋁ q) ⋀ ~ q] → p is
  • true
  • false
  • true, if r is false
  • None of these
The dual of the statement [p ⋁ (~ q)] ⋀ (~ p) is
  • p ⋁ (~ q) ⋁ ~ q
  • (p ⋀ ~ q) ⋁ ~ p
  • p ⋀ ~ (q ⋁ ~ p)
  • None of the above
Which of the following statement has the truth value 'F'?
  • A quadratic equation has always a real root
  • The number of ways of seating 2 persons in two chairs out of n persons is P(n, 2)
  • The cube roots of unity are in GP
  • None of the above
For the circuit shown below, the boolean polynomial is
Maths-Mathematical Logic and Boolean Algebra-38005.png
  • (~ p ⋁ q) ⋁ (p ⋁ ~ q)
  • (~ p ⋀ q) ⋀ (p ⋀ q)
  • (~ p ⋀ ~ q) ⋀ (q ⋀ p)
  • (~ p ⋀ q) ⋁ (p ⋀ ~ q)
The negation of the statement 'He is rich and happy' is given by
  • he is not rich and not happy
  • he is not rich or not happy
  • he is rich and happy
  • he is not rich and happy
If (p ⋀ ~ q) → (~ p ⋁ q) is false, then the truth values of p, q, and r are respectively
  • T, F and F
  • F, F and T
  • F, T and T
  • T, F and T
The statement ~ (p → q) is equivalent to
  • p ⋀ (~ q)
  • ~ p ⋀ q
  • p ⋀ q
  • ~ p ⋀ ~ q
  • p ⋁ q
~ p ⋀ q is logically equivalent to
  • p → q
  • q → p
  • ~ (p → q)
  • ~ (q → p)
~ [p ↔ q] is
  • a tautology
  • a contradiction
  • Neither (a) nor (b)
  • Either (a) or (b)
~[(p ⋀ q) → (~p ⋁ q)] is
  • a tautology
  • a contradiction
  • Neither (a) nor (b)
  • Either (a) or (b)
(p ⋀ ~ q) ⋀ (~ p ⋀ q) is
  • a tautology
  • a contradiction
  • Both (a) and (b)
  • Neither (a) nor (b)
The contrapositive of 'If two triangles are identical, then these are similar' is
  • If two triangles are not similar, then these are not identical
  • If two triangles are not, then these are not similar
  • If two triangles are not identical, then these are similar
  • If two triangles are not similar, then these are identical
Which of the following is not a statement in logic ?
I. Earth is a planet.
II. Plants are living objects.
III . √-3 is a rational number.
IV. x2 - 5x + 6 < 0, where x ϵ - R
  • I
  • III
  • II
  • IV
The function f(x1, x2, x3) satisfying f(x1, x2, x3) = 1 at x1 = 1, x2 = x3 = 0, is
  • x1' ∙ x2
  • x1 ∙ x2 '
  • (x1 + x2 + x3)' ∙x2
  • (x1' + x3)∙ x3
0:0:1


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