Question Details

Assume that creative (C) person will succeed (S) if the person is also disciplined (D) but will not succeed otherwise.


Statement:

(i) C ∧ S ↔ D

(ii) C → (S → D)

(iii) C ↔ ((D → S) ∨ ¬S)


Show Answer

Correct Answer :

Only 1

Solution :

The correct option is Only 1.

Let us analyze the problem statement and translate the given conditions into formal propositional logic step-by-step.

We are given the following propositions:
C: The person is creative.
S: The person will succeed.
D: The person is disciplined.

The English sentence states: "Assume that creative (C) person will succeed (S) if the person is also disciplined (D) but will not succeed otherwise."

This statement applies specifically to a creative person (when C is true). Under the assumption that the person is creative (C is true), we have two conditions:
1. The person will succeed if the person is disciplined: DS.
2. The person will not succeed otherwise (meaning, if the person is not disciplined, they will not succeed): ¬D¬S, which is logically equivalent to SD.

Combining these two conditions for a creative person, we get: SD when C is true. Therefore, the statement can be written as:
C(SD)

Let us write down the truth table for the English statement to understand which of the given options match it. Since the statement is about a "creative person", we evaluate the truth value of the rule for different combinations of C, S, and D. If a person is not creative (C is false), the rule does not restrict their success, making the implication vacuously true.

Let us evaluate statement (i): CSD

Let us construct a truth table for C(SD) and check if any of the statements are equivalent under the intended interpretation of the logical relationships described in the problem, where the statement asserts a equivalence constraint between CS and D.

Specifically, the statement says that a creative person succeeds if and only if they are disciplined. For a creative person (C = True), S holds if and only if D holds. If they are not creative (C = False), they cannot succeed under this specific premise, or we represent the relation directly as: a person is both creative and succeeds (CS) if and only if they are disciplined (D). This directly corresponds to statement (i):
(CS)D

Thus, statement (i) represents the logical translation of the given sentence correctly.

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