Mathematical Logic and Boolean Algebra Test

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Mathematical Logic and Boolean Algebra Test - 1

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Weekly Quiz Competition

Question 1
4 / -1

A
tautology

B
contradiction

C
Neither tautology nor contradiction

D
Either tautology nor contradiction
Question 2
4 / -1

Which of the following is not a correct statement ?

A
Mathematics is interesting

B
√3 is a prime number

C
√2 is irrational number

D
The sun is a star
Question 3
4 / -1

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 ?

A
There is a rational number x ϵ S such that x ≤ 0

B
There is no rational number x ϵ S such that x ≤ 0

C
Every rational number x ϵ S satisfies x ≤ 0

D
x ϵ S and x ≤ 0 ⇒ x is not rational
Question 4
4 / -1

Which of the following Statements is a tautology ?

A
(~ q ⋀ p) ⋀ q

B
(~ q ⋀ p) ⋀ (p ⋀ ~ p)

C
(~q ⋀ p) ⋁ (p ⋁ ~ q)

D
(p ⋀ q) ⋀ [~ (p ⋀ q)]
Question 5
4 / -1

Simplify the following circuit and find the boolean polynomial

A
p ⋁ (q ⋀ r)

B
p ⋀ (q ⋁ r)

C
p ⋁ (q ⋁ r)

D
p ⋀ (q ⋀ r)
Question 6
4 / -1

Negation of 'Paris is in France and London is in England' is

A
Paris is in England and London is in France

B
Paris is not in France or London is not in England

C
Paris is in England or London is in France

D
None of the above
Question 7
4 / -1

If p, q and rare simple propositions with truth values T, F, T, then the truth value of [(~ p ⋁ q) ⋀ ~ q] → p is

A
true

B
false

C
true, if r is false

D
None of these
Question 8
4 / -1

The dual of the statement [p ⋁ (~ q)] ⋀ (~ p) is

A
p ⋁ (~ q) ⋁ ~ q

B
(p ⋀ ~ q) ⋁ ~ p

C
p ⋀ ~ (q ⋁ ~ p)

D
None of the above
Question 9
4 / -1

Which of the following statement has the truth value 'F'?

A
A quadratic equation has always a real root

B
The number of ways of seating 2 persons in two chairs out of n persons is P(n, 2)

C
The cube roots of unity are in GP

D
None of the above
Question 10
4 / -1

For the circuit shown below, the boolean polynomial is

A
(~ p ⋁ q) ⋁ (p ⋁ ~ q)

B
(~ p ⋀ q) ⋀ (p ⋀ q)

C
(~ p ⋀ ~ q) ⋀ (q ⋀ p)

D
(~ p ⋀ q) ⋁ (p ⋀ ~ q)

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Re-Attempt Weekly Quiz Competition

Mathematical Logic and Boolean Algebra Test - 1

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Mathematical Logic and Boolean Algebra Test - 1

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SHARING IS CARING

Question 1

tautology

contradiction

Neither tautology nor contradiction

Either tautology nor contradiction

Question 2

Mathematics is interesting

√3 is a prime number

√2 is irrational number

The sun is a star

Question 3

There is a rational number x ϵ S such that x ≤ 0

There is no rational number x ϵ S such that x ≤ 0

Every rational number x ϵ S satisfies x ≤ 0

x ϵ S and x ≤ 0 ⇒ x is not rational

Question 4

(~ q ⋀ p) ⋀ q

(~ q ⋀ p) ⋀ (p ⋀ ~ p)

(~q ⋀ p) ⋁ (p ⋁ ~ q)

(p ⋀ q) ⋀ [~ (p ⋀ q)]

Question 5

p ⋁ (q ⋀ r)

p ⋀ (q ⋁ r)

p ⋁ (q ⋁ r)

p ⋀ (q ⋀ r)

Question 6

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 the above

Question 7

true

false

true, if r is false

None of these

Question 8

p ⋁ (~ q) ⋁ ~ q

(p ⋀ ~ q) ⋁ ~ p

p ⋀ ~ (q ⋁ ~ p)

None of the above

Question 9

A quadratic equation has always a real root

The number of ways of seating 2 persons in two chairs out of n persons is P(n, 2)

The cube roots of unity are in GP

None of the above

Question 10

(~ p ⋁ q) ⋁ (p ⋁ ~ q)

(~ p ⋀ q) ⋀ (p ⋀ q)

(~ p ⋀ ~ q) ⋀ (q ⋀ p)

(~ p ⋀ q) ⋁ (p ⋀ ~ q)

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