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[Propositional Logic]

Assertion (A): The Equivalence expression is p ↔ q.

Reason (R): An Equivalence Statement always gives the final result as Contingencies.

ID: #24957 Competency focused Practice Questions ISC Class XII Computer Science 4 views

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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

[Propositional Logic]

Assertion (A): The Equivalence expression is p ↔ q.

Reason (R): An Equivalence Statement always gives the final result as Contingencies.

(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 Equivalence expression is p ↔ q

This statement is true.

In propositional logic:

p ↔ q

is called the:

Biconditional statement
Logical equivalence statement

It means:

p if and only if q

Truth Table of p ↔ q:

p	q	p ↔ q
T	T	T
T	F	F
F	T	F
F	F	T

Therefore:

Assertion (A) is TRUE

Step 2: Understanding Reason (R)

An Equivalence Statement always gives the final result as Contingencies.

This statement is false.

Why?

In propositional logic:

Tautology → Always true
Contradiction → Always false
Contingency → Sometimes true and sometimes false

An equivalence expression does NOT always produce contingency.

Depending on the logical statements involved, it may result in:

Tautology
Contradiction
Contingency

Example:

(p → q) ↔ (~q → ~p)

This expression is always TRUE, so it becomes a:

Tautology

Hence the reason statement is incorrect.

Reason (R) is FALSE

Important Concept:

Logical Result	Meaning
Tautology	Always True
Contradiction	Always False
Contingency	Sometimes True, Sometimes False

Final Conclusion:

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

Correct Answer: (c)

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Q [Propositional Logic] Assertion (A): The Equivalence expression is p ↔ q. Reason (R): An Equivalence Statement always gives the final result as Contingencies.