JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 4 - MCQExams.com

~(p⇒ q) ⇔~ p ˅~ q is
  • A tautology
  • A contradiction
  • Neither a tautology nor a contradiction
  • Cannot come to any conclusion
(p ˄~q) ˄ ( ~p ˅ q) is
  • A contradiction
  • A tautology
  • Either (a) or (b)
  • Neither (a) nor (b)
Which of the following is not logically equivalent to the proposition: \ A real number is either rational or irrational\ ?
  • If a number is neither rational nor irrational then it is not real
  • If a number is not a rational or not an irrational, then it is not real
  • If a number is not real, then it is neither rational nor irrational
  • If a number is real, then it is rational or irrational
If p : It rains today, q : I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition?
If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie,
  • ~(p ˄ q) ⇒ (r ˄s)
  • ~(p ˄~q) ⇒ (r ˄S)
  • ~(p ˄q) ⇒ (r ˅ s)
  • None of these
The negation of the compound proposition p ˅ (~ p ˅ q) is
  • (p ˄~q) ˄~p
  • (p ˄~q) ˅~ p
  • (p ˅~ q) ˅~ p
  • None of these
Which of the following is true?
  • p ⇒q ≡ ~p ⇒ ~q
  • ~(p ⇒~q)≡~p˄q
  • ~ (~p⇒ ~q)≡ ~p˄q
  • ~(p ⇔ q) ≡ [ ~ (p⇒ q)˄~ (q⇒ p)]
~(p ˅ q) ˅ (~ p ˄q) is logically equivalent to
  • ~p
  • p
  • q
  • ~q
The inverse of the proposition (p ˄ ~q) ⇒ r is
  • ~r⇒ ~p˅q
  • ~p˅q⇒ ~r
  • r⇒ p˄ ~q
  • None of these
When does the current flow through the following circuit
Maths-Mathematical Logic and Boolean Algebra-38086.png
  • p, q, r should be closed
  • p, q, r should be open
  • Always
  • None of these
Which Venn diagram represents the truth of the statement \ All students are hard working\
Where U = Universal set of human beings
S = Set of all students
H = Set of all hard workers

  • Maths-Mathematical Logic and Boolean Algebra-38087.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38088.png

  • Maths-Mathematical Logic and Boolean Algebra-38089.png
  • None of these
Which Venn diagram represents the truth of the statements \ No child is naughty\ Where
U = Universal set of human beings
C = Set of children
N = Set of naughty persons

  • Maths-Mathematical Logic and Boolean Algebra-38091.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38092.png

  • Maths-Mathematical Logic and Boolean Algebra-38093.png
  • None of these
Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement \ Suman is brilliant and dishonest if and only if Suman is rich\ can be expressed as
  • ~ P ˄ (Q ↔~ R)
  • ~ (Q ↔(P ˄~R))
  • ~ Q ↔~P˄R
  • ~ (P˄~R) ↔ Q
Which Venn diagram represents the truth of the statement \ Some teenagers are not dreamers\

  • Maths-Mathematical Logic and Boolean Algebra-38096.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38097.png

  • Maths-Mathematical Logic and Boolean Algebra-38098.png
  • None of these
Which of the following Venn diagram corresponds to the statement
\ All mothers are women\
(M is the set of all mothers, W is the set of all women)

  • Maths-Mathematical Logic and Boolean Algebra-38099.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38100.png

  • Maths-Mathematical Logic and Boolean Algebra-38101.png

  • Maths-Mathematical Logic and Boolean Algebra-38102.png
The negative of q ˅~(p ˄r) is
  • ~ q ˄~(p ˄r)
  • ~ q ˄(p ˄r)
  • ~q ˅ (p ˅ r)
  • None of these
The proposition (p ⇒ ~p) ˄ (~p ⇒ p) is a
  • Tautology and contradiction
  • Neither tautology nor contradiction
  • Contradiction
  • Tautology
Which of the following is always true?
  • (p⇒ q) ≡ ~q⇒ ~p
  • ~(p ˅ q) ≡˅p˅ ~q
  • ~(p⇒q) ≡ p˄ ~q
  • ~(p ˅ q) ≡~p ˄~q
The contrapositive of (p ˅ q) = r is
  • r⇒ (p˅q)
  • ~r⇒ (p ˅ q)
  • ~r⇒ ~p˄ ~q
  • p ⇒(q ˅ r)
If p⇒ (~p ˅ q) is false, the truth values of p and q arerespectively
  • F, T
  • F, F
  • T, T
  • T, F
Which of the following is not a proposition?
  • √3 is a prime
  • √2 is irrational
  • Mathematics is interesting
  • 5 is an even integer
(p ˄~q) ˄ (~p ˄q) is
  • A tautology
  • A contradiction
  • Both a tautology and a contradiction
  • Neither a tautology nor a contradiction
~p ˄ q is logically equivalent to
  • p → q
  • q → p
  • ~(p → q)
  • ~(q → p)
Which of the following is the inverse of the proposition: \ If a number is a prime then it is odd.\
  • If a number is not a prime then it is odd
  • If a number is not a prime then it is not odd
  • If a number is not odd then it is not a prime
  • If a number is not odd then it is a prime
Let p : roses are red and q : the sun is a star. Then theverbal translation is (~p) ˅ q is
  • Roses are not red and the sun is not a star
  • It is not true that roses are red or the sun is not a star
  • It is not true roses are red and the sun is not a star
  • Roses are not red or the sun in a star
  • It is not true that roses are red and the sun is a star
The statement p → (q → p) is equivalent to
  • p → (p ˅ q)
  • p → (p ˄q)
  • p → (p ↔ q)
  • p → (p → q)
The statement p → (~q) is equivalent to
  • q → p
  • ~q ˅~p
  • p ˄~q
  • ~q → p
  • ~p ˅ q
Which of the following statements is a tautology?
  • (~q˄p)˄q
  • (~q ˄p) ˄(p ˄~p)
  • (~q ˄p) ˅ (p ˅~p)
  • (p ˄q) ˄ (~(p ˄q))
The negation of (p ˅~q) ˄q is
  • (~p ˅ q) ˄ ~q
  • (p ˄~q) ˅ q
  • (~p ˄ q)˅~q
  • (~p ˄~q)˄ ~q
If it is raining, then I will not come. Give its contrapositive
  • If I will come, then it is not raining
  • If I will not come, then it is raining
  • If I will not come, then it is not raining
  • If I will came, then it is raining
The negation of p → (~p ˅ q) is
  • p ˅ (p ˅~q)
  • p →~ (p ˅ q)
  • p → q
  • p ˄ ~ q
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