JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 5 - MCQExams.com

Let S be a non-empty subset of R. Consider the following statement?
p : There is a rational number x ϵ Ssuch that x>0.
which of the following statements is the negation of thestatement p

  • Maths-Mathematical Logic and Boolean Algebra-38122.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38123.png

  • Maths-Mathematical Logic and Boolean Algebra-38124.png

  • Maths-Mathematical Logic and Boolean Algebra-38125.png
Let p : 7 is not greater than 4and q: Paris is in Francebe two statements. Then, ~(p ˅ q) is the statement
  • 7 is greater than 4 or Paris is not in France
  • 7 is not greater than 4 and Paris is not in France
  • 7 is not greater than 4 and Paris is in France
  • 7 is not greater than 4 or Paris is not in France
  • 7 is greater than 4 and Paris is not in France
If S (p, q, r) = (~p) ˅ [~ (q ˄r)] is a compound statement, then S (~p, ~ q, ~ r) is
  • ~S (p, q, r)
  • S (p, q, r)
  • p ˅ (q ˄ r)
  • p ˅ (q ˅ r)
  • S (p, q, ~ r)
Ram secures 100 marks in maths, then he will get amobile. The converse is
  • If Ram gets a mobile, then he will not secures 100 marks
  • If Ram does not get a mobile, then he will secures 100 marks
  • If Ram will get a mobile, then he secures 100 marks in maths
  • None of these
The negation of the statement \ If I become a teacher, then I will open a school\ , is
  • I will become a teacher and I will not open a school
  • Either I will not become a teacher or I will not open a school
  • Neither I will become a teacher nor I will open a school
  • I will not become a teacher or I will open a school
In Boolean Algebra, the zero element \'0\'
  • Has two values
  • Is unique
  • Has atleast two values
  • None of these
In Boolean Algebra, the unit element \'1\'
  • Has two values
  • Is unique
  • Has atleast two values
  • None of these
In a Boolean Algebra B, for all x in B, x ˅ x =
  • 0
  • 1
  • x
  • None of these
In a Boolean Algebra B, for all x in B, x ˄x =
  • 0
  • 1
  • x
  • None of these
In a Boolean Algebra B, for all x in B, x ˅1=
  • 0
  • 1
  • x
  • None of these
In a Boolean Algebra B, for all x, y in B, x ˅ (x ˄ y) =
  • y
  • x
  • 1
  • 0
In a Boolean Algebra B, for all x, y in B, x ˄ (x ˅ y) =
  • y
  • x
  • 1
  • 0
In a Boolean Algebra B, for all x in B, (xʹ)ʹ =
  • x'
  • x
  • 1
  • 0
In a Boolean Algebra B, for all x, y in B, (x ˅ y)ʹ =
  • x' ˅ y'
  • x' ˄ y'
  • 1
  • None of these
In a Boolean Algebra B, for all x, y in B, (x ˄ y)\' =
  • x' ˄y'
  • x' ˅ y'
  • 1
  • None of these
In a Boolean Algebra B, for all x, in B, Oʹ is equal to
  • 0
  • 1
  • x. 0
  • None of these
In a Boolean Algebra B, for all x, in B, 1\' =
  • 0
  • 1
  • x ˄ 1
  • None of these
Dual of (xʹ ˅ y\')\' =x ˄ y is
  • (x' ˅ y')=x ˅ y
  • (x' ˄ y')'=x ˅ y
  • (x' ˄ y')'=x ˄ y
  • None of these
Dual of x ˅ (y ˄x) = x is
  • x ˄(y ˅ x)= x
  • x ˄ (y ˄ x)=x
  • (x ˅ y) ˄(x ˅x) = x
  • None of these
Let B=(p, q, r, ) and let two binary operations be denoted by \'˅\' and \'˄\' or `+\' or \'.\', then
  • p ˅ p' = 0
  • p ˄ p' = 1
  • p ˅ p' =1
  • None of these
An OR gate is the Boolean function defined of

  • Maths-Mathematical Logic and Boolean Algebra-38155.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38156.png

  • Maths-Mathematical Logic and Boolean Algebra-38157.png

  • Maths-Mathematical Logic and Boolean Algebra-38158.png
A NOT gate is the Boolean function defined by

  • Maths-Mathematical Logic and Boolean Algebra-38159.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38160.png

  • Maths-Mathematical Logic and Boolean Algebra-38161.png
  • None of these
Negation of the proposition: If we control population growth, we prosper
  • If we do not control population growth, we prosper
  • If we control population growth, we do not prosper
  • We control population but we do not prosper
  • We do not control population, but we prosper
Which Venn diagram represents the truth of the statement: \ All smokers are drinkers and all drinkers are smokers\

  • Maths-Mathematical Logic and Boolean Algebra-38163.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38164.png

  • Maths-Mathematical Logic and Boolean Algebra-38165.png
  • None of these
For the circuits shown below, the Boolean polynomial is
Maths-Mathematical Logic and Boolean Algebra-38167.png

  • Maths-Mathematical Logic and Boolean Algebra-38168.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38169.png

  • Maths-Mathematical Logic and Boolean Algebra-38170.png

  • Maths-Mathematical Logic and Boolean Algebra-38171.png

Maths-Mathematical Logic and Boolean Algebra-38173.png
  • Mathematics is interesting implies that Mathematics is difficult
  • Mathematics is interesting implies and is implied by Mathematics is difficult
  • Mathematics is interesting and Mathematics is difficult
  • Mathematics is interesting or Mathematics is difficult
An AND gate is the Boolean function defined by

  • Maths-Mathematical Logic and Boolean Algebra-38175.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38176.png

  • Maths-Mathematical Logic and Boolean Algebra-38177.png

  • Maths-Mathematical Logic and Boolean Algebra-38178.png
The output of the circuit is
Maths-Mathematical Logic and Boolean Algebra-38179.png

  • Maths-Mathematical Logic and Boolean Algebra-38180.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38181.png

  • Maths-Mathematical Logic and Boolean Algebra-38182.png

  • Maths-Mathematical Logic and Boolean Algebra-38183.png

  • Maths-Mathematical Logic and Boolean Algebra-38184.png
Statement-1 : ~(p ↔~q) is equivalent to p ↔ q.
Statement-2 : ~(p ↔~q) is a tautology.
  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
  • Statement 1 is true, statement 2 is false
  • Statement 1 is true, statement 2 is true
Let p be the statement \ x is an irrational number\ , q bethe statement \ y is a transcendental number\ , and r be the statement \ x is a rational number if y is a transcendental number\ .
Statement-1: r is equivalent to either q or p.
Statement-2: r is equivalent to ~(p ↔~ q).
  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
  • Statement 1 is true, statement 2 is false
  • Statement 1 is true, statement 2 is true
0:0:1


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