[tex]\begin{array}{c|c|c|c} p & q & \neg q & p \land \neg q \\ T & T & F & F \\ T & F & T & T \\ F & T & F & F \\ F & F & T & F \end{array}[/tex]
[tex]\begin{array}{c|c|c|c} t & s & \neg t & \neg t \implies s \\ T & T & F & T \\ T & F & F & T \\ F & T & T & T \\ F & F & T & F \end{array}[/tex]
[tex]\begin{array}{c|c|c}p\land \neg q & \neg t \implies s & (p \land \neg q) \implies (\neg t \implies s) \\T & T & T \\ T & F & F \\ F & T & T \\ F & F & T \end{array}[/tex]
The given logical statement is false when [tex]p\land\neg q[/tex] and [tex]\neg t\implies s[/tex] are true and false, respectively.
- [tex]p\land\neq g[/tex] is true when [tex]p[/tex] is true and [tex]q[/tex] is false
- [tex]\neg t \implies s[/tex] is false when both [tex]t[/tex] and [tex]s[/tex] are false
