Tautology MCQ Quiz in मराठी - Objective Question with Answer for Tautology - मोफत PDF डाउनलोड करा

Last updated on Mar 11, 2025

पाईये Tautology उत्तरे आणि तपशीलवार उपायांसह एकाधिक निवड प्रश्न (MCQ क्विझ). हे मोफत डाउनलोड करा Tautology एमसीक्यू क्विझ पीडीएफ आणि बँकिंग, एसएससी, रेल्वे, यूपीएससी, स्टेट पीएससी यासारख्या तुमच्या आगामी परीक्षांची तयारी करा.

Latest Tautology MCQ Objective Questions

Top Tautology MCQ Objective Questions

Tautology Question 1:

For any two statements p and q, the negation of the expression \(p \vee (\sim p \wedge q)\) is?

  1. \(p \wedge q\)
  2. \(p \leftrightarrow q\)
  3. \(\sim p \vee \sim q\)
  4. \(\sim p \wedge \sim q\)

Answer (Detailed Solution Below)

Option 4 : \(\sim p \wedge \sim q\)

Tautology Question 1 Detailed Solution

\(\sim (p \vee (\sim p \wedge q))\)

\(= \sim p \wedge \sim (\sim p \wedge q)\)

\(= \sim p \wedge (p \vee \sim q)\)

\(= (\sim p \wedge p) \vee (\sim p \wedge \sim q)\)

\(= F \vee (\sim p \wedge \sim q)\)

\(= (\sim p \wedge \sim q)\)

Tautology Question 2:

The expression \(\sim(\sim p \rightarrow q)\) is logically equivalent to

  1. \(\sim p \land \sim q\)
  2. \(p \land q\)
  3. \(\sim p \land q\)
  4. \(p \land \sim q\)

Answer (Detailed Solution Below)

Option 1 : \(\sim p \land \sim q\)

Tautology Question 2 Detailed Solution

\(p\) \(q\) \(\sim p\) \(\sim p \to q\) \(\sim(\sim p \to q)\) \((\sim p \land \sim q)\)

T F T F T

T T F F F

F T F T T

F F T T F

Tautology Question 3:

The Boolean expression \(\left( p \wedge q \right) \vee \left( p \vee \sim q \right) \wedge \left( \sim p \wedge \sim q \right)\) is equivalent to :

  1. \( p \wedge \sim q \)
  2. \( p \vee \sim q \)
  3. \( \sim p \wedge \sim q \)
  4. \( p \wedge q \)

Answer (Detailed Solution Below)

Option 3 : \( \sim p \wedge \sim q \)

Tautology Question 3 Detailed Solution

By Using Truth Tables for the mentioned Boolean expression we prove that the truth table for \( \sim p \wedge \sim q \) matches. Hence the correct answer is Option C

Tautology Question 4:

The given circuit is equivalent to

qImage67165d28b1312a63fccda0ad

  1. qImage67165d29b1312a63fccda0af
  2. qImage67165d29b1312a63fccda0b2
  3. qImage67165d2ab1312a63fccda0b3
  4. qImage67165d2ab1312a63fccda0b4

Answer (Detailed Solution Below)

Option 4 : qImage67165d2ab1312a63fccda0b4

Tautology Question 4 Detailed Solution

Answer : 4

Solution :

The symbolic form of the given circuit is

(p ~ q ~ r) (p (q ∧ r))

≡ p [(~ q ~ r) ∧ (q ∧ r)] ...[Distributive law]

≡ p [~ (q ∧ r) ∧ (q Ʌ r)] ...[De Morgan's law]

≡ p ∨ F ....[Complement law]

p ...[Identity law]

Tautology Question 5:

The logical statement [~(~p ∨ q) ∨ (p ∧ r)] ∧ (~ q ∧ r) is equivalent to

  1. (p ∧ r) ∧ ~ q
  2. (p ∧ ~ q) ∨r
  3. ~ p ∨ r
  4. ~ p ∧ r

Answer (Detailed Solution Below)

Option 1 : (p ∧ r) ∧ ~ q

Tautology Question 5 Detailed Solution

Answer : 2

Solution :

[~(~ p ∨ q) (p ∧ r)] ∧ (~ q ∧ r)

≡ [(p  ~ q) (p ∧ r)] (~ q ∧ r)...[De Morgan's law]

≡ ∧ (~ q ∨ r) ∧ (~ q ∧ r) ...[Distributive law]

≡ ∧ [(~ q ∨ r) ∧ ~ g] r ...[Associative law]

≡  (~ q) ∧ r.... [Absorption law]

(p ∧ r) ∧ ~ q...Commutative law]

Tautology Question 6:

For the statements p and q, consider the following compound statements:

(a) (~q∧(p → q)) → ~p

(b) ((p∨q))∧~p) → q

Then which of the following statements is correct?

  1. (a) is a tautology but not (b)
  2. (a) and (b) both are not tautologies
  3. (a) and (b) both are tautologies
  4. (b) is a tautology but not (a)

Answer (Detailed Solution Below)

Option 3 : (a) and (b) both are tautologies

Tautology Question 6 Detailed Solution

Concept:

Tautology is a formula or assertion that is true in every possible interpretation

Calculation:

Given, (~q∧(p → q)) → ~p

solved-paper-maths-2021-shift-2-jee-main-24-feb
∴ (a) is tautology.

((p∨q))∧~p) → q

solved-paper-2021-maths-shift-2-jee-main-24-feb
∴ (b) is tautology.

(a) and (b) both are tautologies.

The correct answer is Option 3.

Tautology Question 7:

The negation of the statement ~p∧(p∨q) is∶

  1. ~p∧q
  2. p∧~q
  3. ~p∨q
  4. p∨∼q

Answer (Detailed Solution Below)

Option 4 : p∨∼q

Tautology Question 7 Detailed Solution

Calculation:

Given, ~p∧(p∨q)

∴ Negation of ~p∧(p∨q) is

∼[~p∧(p∨q)]

≡ p ∨ ∼(p ∨ q)

≡ p ∨ (∼p ∧ ∼q)

≡ (p ∨ ∼p) ∧ (p ∨ ∼q)

≡ T ∧ (p ∨ ∼q), where T is tautology.

≡ p ∨ ∼q

∴ The negation of ~p∧(p∨q) is p ∨ ∼q.

The correct answer is Option 4.

Tautology Question 8:

Which of the following is logically equivalent to ~ (p ⇔ q) 

  1. (~p) ⇔ q
  2. ~p ⇔ ~q 
  3. → ~ q
  4.  q 

Answer (Detailed Solution Below)

Option 1 : (~p) ⇔ q

Tautology Question 8 Detailed Solution

Calculation:

We know that ​p ⇔ q = (p ⇒ q) ∧ (q p)

= (~ p ∨ q) ∧ (~ q ∨ p)

∴ ~ (p ⇔ q)

= ~(~ p ∨ q) ∨ ~(~ q ∨ p)

= (p ∧ ~q) ∨ (q ∧ ~p)​

p q (p ∧ ~q) ∨ (q ∧ ~p) (~p) ⇔ q ~p ⇔ ~q  → ~ q   q
T T F F T F T
T F T T F T F
F T T T F T T
F F F F T T T

From truth table,  ~ (p ⇔ q) = (~p) ⇔ q

∴ (~p) ⇔ q is logically equivalent to ~ (p ⇔ q).

The correct answer is Option 1.

Tautology Question 9:

Let p and q are two statements then p \(\leftrightarrow \) q is equivalent to

  1. (p' ∧ q') → q
  2. (p' ∧ q') ∨ (p q)
  3. (p' ∨ q') p
  4. (p' ∧ q')  (p q)

Answer (Detailed Solution Below)

Option 2 : (p' ∧ q') ∨ (p q)

Tautology Question 9 Detailed Solution

Calculation:

Option 1: (p' ∧ q')→q

It means that if both p and q are false, then q is true.

This is not equivalent to p ↔ q.

Option 2: (p' ∧ q') ∨ (p ∧ q)

It means that either both p and q are false, or both p and q are true.

This is exactly what p ↔ q represents.

Option 3: (p' ∨ q') → p

It means that if either p or q is false, then p is true.

This is not equivalent to p ↔ q.

Option 4: (p' ∧ q') ∧ (p ∧ q)

It means that both p and q are false and both p and q are true simultaneously, which is a contradiction.

This is not equivalent to p ↔ q.

∴ p \(\leftrightarrow \) q is equivalent to (p' ∧ q') ∨ (p  q).

The correct answer is Option 2.

Tautology Question 10:

Which of the following statements is a tautology?

  1. ((~ p) ∨ q) ⇒ p
  2. ⇒ ((~ p) ∨ q) 
  3. ((~ p) ∨ q) ⇒ q
  4. q ⇒ ((~ p) ∨ q)

Answer (Detailed Solution Below)

Option 4 : q ⇒ ((~ p) ∨ q)

Tautology Question 10 Detailed Solution

Concept:

A statement which is always correct is a tautology.

Calculation:

Truth Table

p

q

~p

~q

(~p) ∨ q

((~p) ∨ q) p

p ((~p) ∨ q)

(~p) ∨ q q

q ((~p) ∨ q)

T

T

F

F

T

T

T

T

T

T

F

F

T

F

T

F

T

T

F

T

T

F

T

F

T

T

T

F

G

T

T

T

F

T

F

T

∴ q ⇒ ((~ p) ∨ q) is a tautology.

The correct answer is Option 4.

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