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JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 5 - MCQExams.com
JEE
Maths
Mathematical Logic And Boolean Algebra
Quiz 5
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
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2)
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Let p : 7 is not greater than 4and q: Paris is in Francebe two statements. Then, ~(p ˅ q) is the statement
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7 is greater than 4 or Paris is not in France
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7 is not greater than 4 and Paris is not in France
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7 is not greater than 4 and Paris is in France
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7 is not greater than 4 or Paris is not in France
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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
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~S (p, q, r)
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S (p, q, r)
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p ˅ (q ˄ r)
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p ˅ (q ˅ r)
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S (p, q, ~ r)
Ram secures 100 marks in maths, then he will get amobile. The converse is
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If Ram gets a mobile, then he will not secures 100 marks
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If Ram does not get a mobile, then he will secures 100 marks
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If Ram will get a mobile, then he secures 100 marks in maths
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None of these
The negation of the statement \ If I become a teacher, then I will open a school\ , is
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I will become a teacher and I will not open a school
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Either I will not become a teacher or I will not open a school
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Neither I will become a teacher nor I will open a school
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I will not become a teacher or I will open a school
In Boolean Algebra, the zero element \'0\'
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Has two values
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Is unique
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Has atleast two values
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None of these
Explanation
It is obvious
In Boolean Algebra, the unit element \'1\'
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Has two values
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Is unique
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Has atleast two values
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x in B, x ˅ x =
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0
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1
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x
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x in B, x ˄x =
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0
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1
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x
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x in B, x ˅1=
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0
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1
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x
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x, y in B, x ˅ (x ˄ y) =
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y
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x
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1
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0
Explanation
It is obvious
In a Boolean Algebra B, for all x, y in B, x ˄ (x ˅ y) =
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y
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x
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1
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0
Explanation
It is obvious
In a Boolean Algebra B, for all x in B, (xʹ)ʹ =
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x'
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x
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1
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0
Explanation
It is obvious
In a Boolean Algebra B, for all x, y in B, (x ˅ y)ʹ =
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x' ˅ y'
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x' ˄ y'
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1
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x, y in B, (x ˄ y)\' =
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x' ˄y'
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x' ˅ y'
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1
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x, in B, Oʹ is equal to
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0
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1
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x. 0
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None of these
Explanation
It is obvious
In a Boolean Algebra B, for all x, in B, 1\' =
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0
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1
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x ˄ 1
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None of these
Explanation
It is obvious
Dual of (xʹ ˅ 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
Dual of x ˅ (y ˄x) = x is
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x ˄(y ˅ x)= x
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x ˄ (y ˄ x)=x
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(x ˅ y) ˄(x ˅x) = x
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None of these
Let B=(p, q, r, ) and let two binary operations be denoted by \'˅\' and \'˄\' or `+\' or \'.\', then
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p ˅ p' = 0
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p ˄ p' = 1
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p ˅ p' =1
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None of these
An OR gate is the Boolean function defined of
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2)
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Explanation
It is definition
A NOT gate is the Boolean function defined by
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2)
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None of these
Explanation
It is definition
Negation of the proposition: If we control population growth, we prosper
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If we do not control population growth, we prosper
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If we control population growth, we do not prosper
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We control population but we do not prosper
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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\
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None of these
For the circuits shown below, the Boolean polynomial is
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2)
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0%
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Mathematics is interesting implies that Mathematics is difficult
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Mathematics is interesting implies and is implied by Mathematics is difficult
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Mathematics is interesting and Mathematics is difficult
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Mathematics is interesting or Mathematics is difficult
An AND gate is the Boolean function defined by
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2)
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Explanation
It is definition
The output of the circuit is
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Statement-1
: ~(p ↔~q) is equivalent to p ↔ q.
Statement-2
: ~(p ↔~q) is a tautology.
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Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
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Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
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Statement 1 is true, statement 2 is false
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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).
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Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
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Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
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Statement 1 is true, statement 2 is false
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Statement 1 is true, statement 2 is true
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