Question

Choose the conditional statement that can be used with its converse to form the following biconditional statement: "It is a leap year if and only if the year has 366 days."
A. If it is not a leap year, then it does not have 366 days.
B. If it is a leap year, then the year has 366 days.
C. If a leap year has 366 days, then this is a leap year. D. If a year does not have 366 days, then it is not a leap year​

Answer 1

Given the biconditional statement: "It is a leap year if and only if the year has 366 days.", the converse to form it is "If the year has 366 days, then this is a leap year". (Right choice: C)

How to determine the propositional form of a sentence

According to logics, propostions are truth bearers that makes sentences true or false. In linguistics, propositions are the meaning of declarative sentences. There are simple and composite propositions, the latter are formed by one simple proposition at least and logic connectors. There are five logic connectors:

1. Conjuction     X ∧ Y   ("and" operator)
2. Disjunction    X ∨ Y   ("or" operator)
3. Negation       ¬ X       ("not" operator)
4. Implication/Conditional          X ⇒ Y      ("if-then" operator)
5. Double implication/Biconditional       X ⇔ Y     ("if-only if" operator)

By logic rules we know that the double implication/biconditional is commutative operator:

(X ⇔ Y) ⇔ (Y ⇔ X)

In addition, a double implication/biconditional has the following equivalence:

(X ⇒ Y) ∧ (Y ⇒ X)

Where Y ⇒ X is the converse of X ⇒ Y.

Therefore, the converse to form the statement "It is a leap year if and only if the year has 366 days" is Y ⇒ X: "If the year has 366 days, then this is a leap year".

To learn more on propositions: https://brainly.com/question/14789062

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