JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 3 - MCQExams.com

In a boolean algebra B with respect to ' + ' and ' ∙', x' denotes the negation of x ϵ B. Then,
  • x - x' = 1 and x ∙ x' = 1
  • x + x' = 1 and x ∙ x' = 0
  • x + x' = 0 and x ∙ x' = 1
  • x + x' = 0 and x ∙ x' = 0
  • x - x' = 1 and x ∙ x' = 0
The boolean expression corresponding to the combinationalcircuit is
Maths-Mathematical Logic and Boolean Algebra-38056.png
  • (x1 + x2 ∙ x3') x2
  • [x1 ∙ (x2 + x3)] + x2
  • [x1 ∙ (x2 + x3')] + x2
  • [x1 ∙ (x2 + x3')] + x3
  • (x1 + x2' ∙ x3)x2
The output of the circuit is
Maths-Mathematical Logic and Boolean Algebra-38057.png
  • x3 ∙ (x1' + x2)
  • (x3' + x∙ x1
  • x3' ∙ (x1 + x2)
  • (x1' + x∙ x3
  • (x1' + x2') ∙ x3
If B is a boolean algebra and a, b ϵ B, then a • (a + b) is equal to
  • a
  • b
  • 1
  • a'
The output of the circuit is
Maths-Mathematical Logic and Boolean Algebra-38058.png
  • (x2 + x∙ [(x1 ∙ x∙x3']
  • (x2 + x3') ∙ [(x1 ∙ x∙x3']
  • (x2 + x+ [(x1 ∙ x∙x3']
  • (x1 + x∙ [(x1 ∙ x∙x3']
Let a be any element in booleanalgebra B. If a + x = 1 and ax = 0, then
  • x = 1
  • x = 0
  • x = a
  • x = a'
The output s as a boolean expression in the inputs x1, x2, and x3 for the logic circuit in the following figure
Maths-Mathematical Logic and Boolean Algebra-38059.png
  • x1 x2' + x2' + x3
  • x1' + x2' x3 + x3
  • (x1 x2)' + x1x2' x3
  • x1 + x2' + x3
  • x1 x2' + x2' x3

Maths-Mathematical Logic and Boolean Algebra-38060.png
  • x ∙ (y' + z)
  • x ∙ (y' + z')
  • x ∙ (y + z)
  • (x + y) ∙ z
  • x ∙ y + z
In a boolean algebra a + (a' ∙ b) is equal to
  • a + b
  • a ∙ b
  • a'
  • b'
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 rational number iff y is transcendental number'.
Statement I r is equivalent to either q or p
Statement II r is equivalent to ~(p ↔ ~ q ).
  • Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I
  • Statement I is correct, Statement II is correct; Statement Ii is not a correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect
  • Statement I is incorrect, Statement II is correct
  • None of these
Which of the following is a statement?
  • Open the door
  • Do your homework
  • Switch on the fan
  • Two plus two is four
Which of the following is not a statement?
  • Roses are red
  • New Delhi is in India
  • Every square is a rectangle
  • Alas! I have failed
Which of the following is an open statement?
  • x is a natural number
  • Give me a glass of water
  • Wish you best of luck
  • Good morning to all
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 rain and I shall go to school
  • None of these
Negation of \ Paris 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 these
Negation of \ 2 + 3 = 5 and 8 < 10\ is
  • 2 + 3 ≠ 5 and < 10
  • 2 + 3 = 5 and 8 ≮ 10
  • 2 + 3 ≠ 5 or 8 ≮ 10
  • None of these
Negation of \ Ram is in Class X or Rashmi is in Class XII\ is
  • Ram is not in class X but Ram is in class XII
  • Ram is not in class X but Rashmi is not in class XII
  • Either Ram is not in Class X or Ram is not in class XII
  • None of these
The conditional (p ˄ q) ⇒ p is
  • A tautology
  • A fallacy i.e., contradiction
  • Neither tautology nor fallacy
  • None of these
Which of the following is a contradiction?
  • (p ˄q) ˄∼ (p ˅ q)
  • p ˅ (~ p ˄ q)
  • (p⇒ q)⇒p
  • None of these
Which of the following is logically equivalent to ~ (~(P ⇒ q)?
  • p ˄ q
  • P ˄ ~ q
  • ~p ˄ q
  • ~ p ˄ ~ q
~ (p ˅ q) is equal to
  • ~ p ˅ ~ q
  • ~ p ˄ ~ q
  • ~ p ˅ q
  • p ˅ ~ q
~ (p ˄ q) is equal to
  • ~ p˅ ~ q
  • ~ p˄ ~ q
  • ~ p ˄ q
  • p ˄ ~ q
(~(~p))˄q is equal to
  • ~ p ˄ q
  • p ˄ q
  • p ˄ ~ q
  • ~p ˄ ~ q
~ (p ˅ (~q)) is equal to
  • ~p˅q
  • (~p)˄q
  • ~p ˄ ~p
  • ~p˄ ~q
~((~p)˄q) is equal to
  • p ˅ (~ q)
  • p˅q
  • p ˄ (~q)
  • ~p˄ ~q
~ ( p ⇔ q) is
  • ~p˄ ~q
  • ~p˅ ~q
  • (p ˄ ~q)˅(~p ˄q)
  • None of these
p ⇒ q can also be written as
  • p⇒ ~q
  • ~ p ˅ q
  • ~q⇒ ~p
  • None of these
If p, q, r are simple propositions with truth values T, F,T, then the truth value of (~p ˅ q) ˄~r ⇒ p is
  • True
  • False
  • True if r is false
  • True if q is true
If (p ˄~r)⇒ (q ˅ r) is false and q and r are both false,then p is
  • True
  • False
  • May be true or false
  • Data insufficient
If p, q, r are simple propositions, then (p ˄q) ˄(q ˄r) is true then
  • p, q, r are all false
  • p, q, r are all true
  • p, q are true and r is false
  • p is true and q and r are false
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