Test: Mathematical Reasoning- 2


25 Questions MCQ Test Mathematics For JEE | Test: Mathematical Reasoning- 2


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Attempt Test: Mathematical Reasoning- 2 | 25 questions in 25 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics For JEE for JEE Exam | Download free PDF with solutions
QUESTION: 1

The contrapositive of (p∨q)→ r is

Solution:

Contrapositive of p→q is ∼q→∼p.
∴ Contrapositive of (p∨q)⇒r  is ∼r⇒∼(p∨q) i.e. ∼r⇒(∼p∧∼q).

QUESTION: 2

The contrapositive of p→(∼q→∼r) is

Solution:
QUESTION: 3

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

Solution:
QUESTION: 4

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

Solution:
QUESTION: 5

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

Solution:
QUESTION: 6

p∧(q∧r) is logically equivalent to

Solution:
QUESTION: 7

Which of the following proposition is a tautology ?

Solution:
QUESTION: 8

The negation of the compound statement p∨(∼p∨q) is

Solution:

QUESTION: 9

The proposition p→∼(p∧∼q) is

Solution:
QUESTION: 10

The proposition (p→∼p)∧(∼p→p) is

Solution:
QUESTION: 11

Which of the following is equivalent to (p∧q) ?

Solution:
QUESTION: 12

Which of the following is logically equivalent to ∼(∼p→q) ?

Solution:

∼(p⇒q)≡p∧∼q
∴ ∼(∼p⇒q) ≡∼p∧∼q

QUESTION: 13

The contrapositive of the inverse of p⇒ ~q is

Solution:

The inverse of p ⇒ ∼q is ∼p ⇒ q 
The contrapositive of ∼p ⇒ q is ∼q ⇒ p. [∴ Contrapositive of p ⇒ q is∼q ⇒ p.]

QUESTION: 14

p→q is logically equivalent to

Solution:
QUESTION: 15

The contrapositive of (∼p∧q)→ is

Solution:
QUESTION: 16

The negation of p∧∼(q∧r) is

Solution:
QUESTION: 17

The negation of q∨∼(p∧r) is

Solution:
QUESTION: 18

Which of the following is a contradiction?

Solution:
QUESTION: 19

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

Solution:
QUESTION: 20

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

Solution:
QUESTION: 21

If p→(q∨r) is false , then the truth values of p , q and r, are respectively

Solution:
QUESTION: 22

The statement p ⇒ p∨q is

Solution:

A tautology is a proposition is always true.

QUESTION: 23

The statement p∨qp∨q is

Solution:
QUESTION: 24

Which of the following sentences is a statement ?

Solution:
QUESTION: 25

Let p and q be two prepositions given by p : I take only bread and butter in breakfast. q : I do not take anything in breakfast. Then , the compound proposition “ I take only bread and butter in breakfast or I do not take anything “ is represented by

Solution:
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