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JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 1 - MCQExams.com
JEE
Maths
Mathematical Logic And Boolean Algebra
Quiz 1
If p is the statement 'Ravi races' and q is the statement `Ravi wins'. Then, the verbal translation of ~ [p ⋁ (~ q)] is
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Ravi does not race and Ravi does not win
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It is not true that Ravi races and that Ravi does not win
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Ravi does not race and Ravi wins
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It is not true that Ravi does not race or that Ravi does not win
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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
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if 2 is not prime, then 3 is not odd
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2 is prime and 3 is not odd
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2 is not prime and 3 is odd
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if 2 is not prime, then 3 is odd
If p ⇒(q ˅ r) is false, then the truth values of p, q, r arerespectively
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T, F, F
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F, F, F
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F, T, T
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T, T, F
The logically equivalent proposition of p ⇔ q is
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(p ˄q) ˅(p ˄ q)
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(p⇒ q) ˄ (q⇒ p)
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(p ˄q) ˅ (q⇒ p)
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(p ˄q)⇒ (q ˅ p)
The false statement in the following is
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p ˄ (~p) is a contradiction
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(p ⇒ q) ⇔ (~q⇒~p) is a contradiction
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~ (~p) ⇔ p is a tautology
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p ˅ (~ p) ⇔ is a tautology
~(p ⋁ q ) ⋁ (~ p ⋀ q) is logically equivalent to
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~q
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~ p
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p
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q
The contrapositive of (p ⋁ q) → r is
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~ r → (p ⋁ q)
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r → (p ⋁ q)
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~ r → (~ p ⋀ ~ q)
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p → (q ⋁ r)
Negation of the conditional, 'If it rains, I shall go to school' is
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It rains and I shall go to school
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It rains and I shall not go to school
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It does not rains and I shall go to school
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None of the above
Dual of (
x
' ⋁ y')' =
x
⋀ y is
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(x' ⋁ y') = x ⋁ y
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(x' ⋀ y')' = x ⋁ y
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(x' ⋀ y') = x ⋀ y
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None of these
The converse of the contrapositive of the conditional p → ~q is
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p → q
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~ p → ~ q
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~ q → p
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~ p → q
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tautology
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contradiction
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Neither tautology nor contradiction
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Either tautology nor contradiction
Which of the following is not a correct statement ?
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Mathematics is interesting
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√3 is a prime number
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√2 is irrational number
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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 ?
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There is a rational number x ϵ S such that x ≤ 0
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There is no rational number x ϵ S such that x ≤ 0
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Every rational number x ϵ S satisfies x ≤ 0
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x ϵ S and x ≤ 0 ⇒ x is not rational
Which of the following Statements is a tautology ?
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(~ q ⋀ p) ⋀ q
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(~ q ⋀ p) ⋀ (p ⋀ ~ p)
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(~q ⋀ p) ⋁ (p ⋁ ~ q)
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(p ⋀ q) ⋀ [~ (p ⋀ q)]
Simplify the following circuit and find the boolean polynomial
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p ⋁ (q ⋀ r)
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p ⋀ (q ⋁ r)
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p ⋁ (q ⋁ r)
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p ⋀ (q ⋀ r)
Negation of 'Paris is in France and London is in England' is
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Paris is in England and London is in France
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Paris is not in France or London is not in England
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Paris is in England or London is in France
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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
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true
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false
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true, if r is false
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None of these
The dual of the statement [p ⋁ (~ q)] ⋀ (~ p) is
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p ⋁ (~ q) ⋁ ~ q
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(p ⋀ ~ q) ⋁ ~ p
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p ⋀ ~ (q ⋁ ~ p)
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None of the above
Which of the following statement has the truth value 'F'?
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A quadratic equation has always a real root
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The number of ways of seating 2 persons in two chairs out of n persons is P(n, 2)
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The cube roots of unity are in GP
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None of the above
For the circuit shown below, the boolean polynomial is
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(~ p ⋁ q) ⋁ (p ⋁ ~ q)
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(~ p ⋀ q) ⋀ (p ⋀ q)
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(~ p ⋀ ~ q) ⋀ (q ⋀ p)
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(~ p ⋀ q) ⋁ (p ⋀ ~ q)
The negation of the statement 'He is rich and happy' is given by
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he is not rich and not happy
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he is not rich or not happy
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he is rich and happy
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he is not rich and happy
If (p ⋀ ~ q) → (~ p ⋁ q) is false, then the truth values of p, q, and r are respectively
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T, F and F
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F, F and T
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F, T and T
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T, F and T
The statement ~ (p → q) is equivalent to
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p ⋀ (~ q)
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~ p ⋀ q
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p ⋀ q
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~ p ⋀ ~ q
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p ⋁ q
~ p ⋀ q is logically equivalent to
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p → q
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q → p
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~ (p → q)
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~ (q → p)
~ [p ↔ q] is
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a tautology
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a contradiction
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Neither (a) nor (b)
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Either (a) or (b)
~[(p ⋀ q) → (~p ⋁ q)] is
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a tautology
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a contradiction
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Neither (a) nor (b)
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Either (a) or (b)
(p ⋀ ~ q) ⋀ (~ p ⋀ q) is
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a tautology
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a contradiction
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Both (a) and (b)
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Neither (a) nor (b)
The contrapositive of 'If two triangles are identical, then these are similar' is
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If two triangles are not similar, then these are not identical
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If two triangles are not, then these are not similar
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If two triangles are not identical, then these are similar
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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.
x
2
- 5
x
+ 6 < 0, where
x
ϵ - R
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I
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III
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II
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IV
The function
f
(
x
1
,
x
2
,
x
3
) satisfying
f
(
x
1
,
x
2
,
x
3
) = 1 at
x
1
= 1,
x
2
=
x
3
= 0, is
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x1' ∙ x2
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x1 ∙ x2 '
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(x1 + x2 + x3)' ∙x2
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(x1' + x3)∙ x3
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