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)
Correct Answer :
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:
: The person is creative.
: The person will succeed.
: 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 is true). Under the assumption that the person is creative ( is true), we have two conditions:
1. The person will succeed if the person is disciplined: .
2. The person will not succeed otherwise (meaning, if the person is not disciplined, they will not succeed): , which is logically equivalent to .
Combining these two conditions for a creative person, we get: when is true. Therefore, the statement can be written as:
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 , , and . If a person is not creative ( is false), the rule does not restrict their success, making the implication vacuously true.
Let us evaluate statement (i):
Let us construct a truth table for 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 and .
Specifically, the statement says that a creative person succeeds if and only if they are disciplined. For a creative person (), holds if and only if holds. If they are not creative (), they cannot succeed under this specific premise, or we represent the relation directly as: a person is both creative and succeeds () if and only if they are disciplined (). This directly corresponds to statement (i):
Thus, statement (i) represents the logical translation of the given sentence correctly.
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