Question

A biconditional statement is the conjunction of two ………. Statements.
A. negative
B. compound
C. connective
D. conditional

Answer 1

Hint: First we recall the definition of biconditional statements. Then, we discuss the properties and truth table of biconditional statements. When we analyze all about the biconditional statements, we will reach our answer.

Complete step-by-step answer:
As we know that the biconditional statement is a binary operation. Biconditional statements are always compound statements.
A biconditional statement will be considered true, when both the parts will have a same truth value.
As we know that the truth table is a mathematical table used to determine whether a compound statement is true or false on the basis of input given. Biconditional statements are represented as “if and only if” statements. A Biconditional operator works in both directions. In mathematics, the biconditional operator is symbolically represented by a double-headed arrow ‘ \[\Leftrightarrow \] ‘.
If we have two input $ X\text{ and Y} $ , then the truth table for a biconditional operator will be

X	Y	Biconditional\[\Leftrightarrow \]
T	T	T
T	F	F
F	T	F
F	F	T

In the above table T indicates true and F indicates false. In a biconditional statement the output is true only if the input values are true or if both the input values are false. For either of the input values being true or false, the value is false. If we combine two conditional statements, we will get a biconditional statement.
When we learn the properties of biconditional statements discussed above, we will get our answer that a biconditional statement is the conjunction of two conditional Statements.
Option D is the correct answer.
Note: Some examples of biconditional statements are-
Example 1- A polygon is a triangle if and only if it has three sides.
Example 2- A triangle is equilateral if and only if it has all sides equal.
Example 3- If we have given two statements:
 $ \begin{align}
  & P:x+5=9 \\
 & q:x=4 \\
\end{align} $
Then, $ p\Leftrightarrow q $ , if and only if both the statements have the same value.