A logical expression seems to be a statement that could be true or false depending on the context, therefore the calculated expression is "[tex]\overline{(p \vee q)} \wedge r[/tex]".
Logical Expression:
Consider that all possible combinations of the [tex]p,q, \ and \ r[/tex] are in the following truth table.
- The objective is to write a logical expression with the given variables [tex]p, q,[/tex] and [tex]r,[/tex] is true only if p and q are false and r is true.
- Given conditions is [tex]p \ and\ q[/tex] are false and r is true. if p is false and q is false then [tex]p \vee q[/tex] is false.
- Next, the complement of [tex]p \vee q[/tex] is [tex]\overline{p \vee q}[/tex] is true, [tex]\overline{p \vee q}[/tex] is true and r is true then [tex]\overline{(p \vee q)} \wedge r[/tex] is true. Therefore, the logical expression is [tex]\overline{(p \vee q)} \wedge r[/tex].
The Truth table of [tex]\overline{(p \vee q)} \wedge r[/tex]satisfying the condition is defined in the attached file.
Find out more information about the expression here:
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