Mathematical Reasoning Test

Result

Mathematical Reasoning Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Let p and q be two propositions. Then the inverse of the implication p→q is

A
p→∼q

B
∼p→q

C
∼p→∼q

D
∼q→p

Solution

inverse of p → q ≡ ∼ p → ∼ q
Question 2
1 / -0

Let p and q be two propositions. Then the contrapositive of the implication p→q is

A
∼ q → ∼ p

B
∼ q → p

C
p ↔ q

D
∼ p → ∼ q

Solution

The contrapositive of p → q ≡ ∼ q → ∼ p
Question 3
1 / -0

Let p and q be two propositions. Then the implication p→q is false ,when

A
p is true and q is false

B
p is true and q is true

C
p is false and q is true

D
both p and q are false

Solution

Since T → F ≡ F
Question 4
1 / -0

Let p and q be two propositions. Then the implication p ↔ ∼ q is true ,when

A
p is false and q is true

B
p is true and q is true

C
both p and q are false

D
None of these

Solution

p q ∼q p ↔ ∼ q

T T F F

T F T T

F T F T

F F T F
Question 5
1 / -0

For any three propositions p , q , and r , the proposition (p ∧ q ) ∧ ( q ∧ r ) is true , when

A
p, q are true and r is false

B
p, q , r a

C
p is true and q, r are false

D
p,q , r are all true

Solution

T∧ T ≡ T

hence p=T , q=T, r=T
Question 6
1 / -0

Let p and q be two propositions. Then the implication ∼( p ↔ q ) is :

A
∼ p ∨ ∼ q

B
(p ∧ ∼ q) ∨ (∼p ∧ q)

C
∼ p ∧ ∼ q

D
none of these

Solution

∼(p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)
Question 7
1 / -0

p ∧ (q ∧ r) is logically equivalent to

A
(p ∨ q ) ∧ r

B
p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r

C
(p ∨ q) ∨ r

D
p → (q ∧ r)

Solution

Associative law
Question 8
1 / -0

∼(∼ p ) ↔ p is

A
a tautology

B
a contradiction

C
neither a contradiction nor a tautology

D
none of these

Solution

∼(∼ p ) ≡ p

T ↔ T ≡ T

F↔ F ≡ T
Question 9
1 / -0

Which of the following is a proposition ?

A
A triangle is a circle and 10 is a prime number

B
I am a lion

C
Logic is an interesting subject

D
A half open door is half closed

Solution

it is a statement which is F.Hence it is a proposition.Other options are open sentences which are not propositions
Question 10
1 / -0

Which of the following proposition is a tautology ?

A
∼p ∧ ( ∼ p ∨ ∼ q)

B
∼ q ∧ (∼ p ∨ ∼ q)

C
(∼ p ∨ ∼ q) ∨ (p ∨ ∼ q)

D
(∼ p ∨ ∼ q) ∧ (p ∨ ∼ q)

Solution

(∼ p ∨ p) ≡ T and ∼ q ∨ q ≡ T Associative law

T ∨ T ≡ T

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Re-Attempt Weekly Quiz Competition

p	q	∼q	p ↔ ∼ q
T	T	F	F
T	F	T	T
F	T	F	T
F	F	T	F

Mathematical Reasoning Test - 6

Result

Mathematical Reasoning Test - 6

Score

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Rank

-

SHARING IS CARING

Question 1

p→∼q

∼p→q

∼p→∼q

∼q→p

Solution

Question 2

∼ q → ∼ p

∼ q → p

p ↔ q

∼ p → ∼ q

Solution

Question 3

p is true and q is false

p is true and q is true

p is false and q is true

both p and q are false

Solution

Question 4

p is false and q is true

p is true and q is true

both p and q are false

None of these

Solution

Question 5

p, q are true and r is false

p, q , r a

p is true and q, r are false

p,q , r are all true

Solution

Question 6

∼ p ∨ ∼ q

(p ∧ ∼ q) ∨ (∼p ∧ q)

∼ p ∧ ∼ q

none of these

Solution

Question 7

(p ∨ q ) ∧ r

p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r

(p ∨ q) ∨ r

p → (q ∧ r)

Solution

Question 8

a tautology

a contradiction

neither a contradiction nor a tautology

none of these

Solution

Question 9

A triangle is a circle and 10 is a prime number

I am a lion

Logic is an interesting subject

A half open door is half closed

Solution

Question 10

∼p ∧ ( ∼ p ∨ ∼ q)

∼ q ∧ (∼ p ∨ ∼ q)

(∼ p ∨ ∼ q) ∨ (p ∨ ∼ q)

(∼ p ∨ ∼ q) ∧ (p ∨ ∼ q)

Solution

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