MCQ Single Best Answer Moderate

Q
[Boolean Algebra]

Assertion (A): The contrapositive of p ⇒ q is q̅ ⇒ p̅.

Reason (R): Contrapositive is the conditional statement, obtained after interchanging antecedent and consequent.

ID: #24958 Competency focused Practice Questions ISC Class XII Computer Science 4 views

Question Info

#24958Q ID

ModerateDifficulty

Competency focused Practice Questions ISC Class XII Computer ScienceTopic

Start Quiz on This Topic

Your Answer

Choose the Best Option

Click any option to instantly check if you're correct.

A Both A and R are true, and R is the correct explanation of A. ✔ ✖
B Both A and R are true, but R is not the correct explanation of A. ✔ ✖
C A is true, but R is false. ✔ ✖
D A is false, but R is true. ✔ ✖

Correct Answer: Option C

Explanation

[Boolean Algebra]

Assertion (A): The contrapositive of p ⇒ q is q̅ ⇒ p̅.

Reason (R): Contrapositive is the conditional statement, obtained after interchanging antecedent and consequent.

(a) Both A and R are true, and R is the correct explanation of A.

(b) Both A and R are true, but R is not the correct explanation of A.

(d) A is false, but R is true.

Correct Answer: (c)

Step 1: Understanding Assertion (A)

The contrapositive of p ⇒ q is q̅ ⇒ p̅

This statement is true.

Formula for Contrapositive:

If p ⇒ q, then Contrapositive = q̅ ⇒ p̅

Steps to form contrapositive:

Interchange antecedent and consequent
Negate both statements

Example:

Original Statement: p ⇒ q Contrapositive: q̅ ⇒ p̅

Therefore:

Assertion (A) is TRUE

Step 2: Understanding Reason (R)

Contrapositive is obtained after interchanging antecedent and consequent.

This statement is false.

Why?

Merely interchanging antecedent and consequent gives:

q ⇒ p

This is called the:

Converse

To form the contrapositive, we must:

Interchange antecedent and consequent
AND negate both propositions

Contrapositive of p ⇒ q = q̅ ⇒ p̅

Important Difference:

Type	Expression
Original Statement	p ⇒ q
Converse	q ⇒ p
Inverse	p̅ ⇒ q̅
Contrapositive	q̅ ⇒ p̅

Conclusion:

Assertion (A) → True ✅
Reason (R) → False ❌

Correct Answer: (c)

Continue Practice

Previous Question No Next

Share This Question

Challenge a friend or share with your study group.

Q [Boolean Algebra] Assertion (A): The contrapositive of p ⇒ q is q̅ ⇒ p̅. Reason (R): Contrapositive is the conditional statement, obtained after interchanging antecedent and consequent.