Answer
The truth value of the provided compound statement with the provided condition is true.
Work Step by Step
The provided compound statement in symbolic form is\[\sim \left( p\leftrightarrow q \right)\].
Substitute, the truth values for simple statements\[p,q,r\] to determine the truth value for the provided compound statement\[\sim \left( p\leftrightarrow q \right)\].
The provided compound statement is a negation of\[\left( p\leftrightarrow q \right)\], which is a conditional statement.
A biconditional statement is true only when the truth values of both the simple statement are same.
Replace with the truth values of a simple statement\[\sim \left( \text{F}\leftrightarrow \text{T} \right)\].
This implies the truth values can be rewritten as \[\sim \left( \text{F} \right)\] or in the simplest form it can be written as \[\text{T}\](true).
Therefore, it can be represented in the table form as:
