Answer
The given statement in symbolic form is\[\left( p\wedge \sim q \right)\vee \sim p\], and it gives truth value as true only when the statement \[p\] is false and\[q\]is also false.
Work Step by Step
Assume the statement:
\[p\]: \[x\le 3\],
\[q\]: \[x\ge 7\].
The given statement first shows the conjunction of the negation of disjunction of the statement\[p\]and the statement\[q\], and the conjunction of \[\left( \sim p\wedge \sim q \right)\] .
Hence, the given statement in symbolic form is:
\[\sim \left( p\vee q \right)\wedge \left( \sim p\wedge \sim q \right)\].
The truth table for the given statement is below:
From above truth table, it is clear that \[\sim \left( p\vee q \right)\wedge \left( \sim p\wedge \sim q \right)\]gives truth value as true only when \[p\]and \[q\] both are false, otherwise, it gives truth value as false.
