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The sentence can be divided into two statements: 'It is not true that \(x<5\) or \(x>8\)' and '\(x \geq 5\) and \(x \leq 8\)'.Let's translate them into logical symbols:- \(P\) be '\(x<5\)'- \(Q\) be '\(x>8\)'- \(R\) be '\(x \geq 5\)'- \(S\) be '\(x \leq 8\)'The entire statement can be written as: 'It is not true that \(P\) or \(Q\)', but \(R\) and \(S\)'. In symbolic form, it can be represented as: \(\neg (P \lor Q) \land (R \land S)\).

A truth table for this compound statement would involve the truth values for each of \(P, Q, R\), and \(S\), the truth value for \(P \lor Q\), the complement of the truth value for \(P \lor Q\), and finally the truth value for the entire compound statement. Here is the truth table:| \(P\) | \(Q\) | \(R\) | \(S\) | \(P \lor Q\) | \(\neg (P \lor Q)\) | \(R \land S\) | \(\neg (P \lor Q) \land (R \land S)\) ||-------|-------|-------|-------|-------------|-------------------|-------------|----------------------------------|| T | T | F | F | T | F | F | F || T | F | F | T | T | F | F | F || F | T | T | F | T | F | F | F || F | F | T | T | F | T | T | T |In the table, 'T' represents 'true' and 'F' represents 'false'.

The compound statement \(\neg (P \lor Q) \land (R \land S)\) is true only when all of \(P, Q, R\), and \(S\) are false. This corresponds to the last row in the truth table, where \(P\) and \(Q\) are false ('It's not true that \(x<5\) or \(x>8\)') and \(R\) and \(S\) are true ('\(x \geq 5\) and \(x \leq 8\)'). So, the conditions under which the compound statement is true are when \(x \geq 5\) and \(x \leq 8\).