Write a short note on Biconditional proposition.

A biconditional proposition, also known as a material equivalence, is a logical statement that asserts that two propositions are logically equivalent. In other words, a biconditional proposition states that two statements are true or false simultaneously, indicating that they are either both true or both false.

Symbolically, a biconditional proposition is represented by the double arrow "↔" and can be expressed as "p if and only if q," where "p" and "q" are two propositions.

For example, the biconditional proposition "It is raining if and only if the ground is wet" asserts that the occurrence of rain is necessary and sufficient for the ground to be wet, and vice versa. Therefore, if it is raining, then the ground is wet, and if the ground is wet, then it is raining. Similarly, if it is not raining, then the ground is not wet, and if the ground is not wet, then it is not raining. Biconditional propositions are commonly used in mathematics, logic, and philosophy to express logical equivalence between statements.