Mathematical Reasoning Test

Result

Mathematical Reasoning Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

The contrapositive of ( ∼p ∧ q) → ∼ r is

A
r → (p ∨ ∼ q)

B
(p ∨ q) → r

C
(p ∧ q) → r

D
none of these

Solution

Contrapositive of p → q is ∼ q → ∼ p
Question 2
1 / -0

The negation of p ∧ ∼ (q ∧ r) is

A
p ∨ (q ∧ r)

B
∼p ∨ (q ∧ r)

C
∼p → ( q ∨ ∼ r)

D
∼p → (q ∧ r)

Solution

∼ (p ∧ q) ≡ ∼ p ∨ ∼ q
Question 3
1 / -0

The negation of q ∨ ∼ (p ∧ r) is

A
q ∨(p ∨ r)

B
∼q ∧ (p ∧ r)

C
∼q ∨ (p ∨ r)

D
∼q ∧ (p ∨ r)

Solution

∼( p ∧ q ) ≡ ∼ p ∨ ∼ q
Question 4
1 / -0

Consider the proposition: “If we control population growth, then we prosper “. Negative of this proposition is

A
If we control population, we do not prosper

B
If we do not control population growth but we prosper

C
We do not control population but we prosper

D
We control population but we do not prosper

Solution

p:we control population growth, q:we prosper.the sentence is of the form p → q.

∼(p → q ) ≡ p ∧ ∼ q
Question 5
1 / -0

Consider the proposition: “If the pressure increases, then volume decreases “. Negative of this proposition is

A
If the pressure does not increase the volume does not decrease

B
If the volume decreases, then the pressure increases

C
If the volume increases, the pressure decreases

D
The pressure increases but volume does not decrease.

Solution

p:The pressure increases; q:Volume decreases.

∼(p → q) ≡ p ∧ ∼ q
Question 6
1 / -0

Which of the following is logically equivalent to p ∧ q ?

A
∼( p→ ∼ q)

B
∼(∼ p ∧ ∼ q)

C
(p ∧ ∼ q)

D
none of these

Solution

∼(∼p ∨ q) since p → q ≡ ∼p ∨ q

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

The negation of the proposition q∨ ∼ (p ∧ r) is

A
q ∧ (p ∧ r)

B
∼q ∧ (p ∧ r)

C
∼q ∧ (∼ p ∧ ∼ r)

D
none of these

Solution

∼(q ∨ ∼ (p ∧ r))

∼q ∧ ( p∧ r) since∼ (p ∨ q) ≡ ∼ p ∧ ∼ q
Question 8
1 / -0

Which of the following sentences is a statement ?

A
Aarushi is a pretty girl

B
2 is the smallest prime number

C
Oh ! It is amazing

D
What are you doing ?

Solution

It is a true statement in mathematics.other options are neither true nor false

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Re-Attempt Weekly Quiz Competition

Mathematical Reasoning Test - 8

Result

Mathematical Reasoning Test - 8

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SHARING IS CARING

Question 1

r → (p ∨ ∼ q)

(p ∨ q) → r

(p ∧ q) → r

none of these

Solution

Question 2

p ∨ (q ∧ r)

∼p ∨ (q ∧ r)

∼p → ( q ∨ ∼ r)

∼p → (q ∧ r)

Solution

Question 3

q ∨(p ∨ r)

∼q ∧ (p ∧ r)

∼q ∨ (p ∨ r)

∼q ∧ (p ∨ r)

Solution

Question 4

If we control population, we do not prosper

If we do not control population growth but we prosper

We do not control population but we prosper

We control population but we do not prosper

Solution

Question 5

If the pressure does not increase the volume does not decrease

If the volume decreases, then the pressure increases

If the volume increases, the pressure decreases

The pressure increases but volume does not decrease.

Solution

Question 6

∼( p→ ∼ q)

∼(∼ p ∧ ∼ q)

(p ∧ ∼ q)

none of these

Solution

Question 7

q ∧ (p ∧ r)

∼q ∧ (p ∧ r)

∼q ∧ (∼ p ∧ ∼ r)

none of these

Solution

Question 8

Aarushi is a pretty girl

2 is the smallest prime number

Oh ! It is amazing

What are you doing ?

Solution

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