Topic: Discrete Mathematics
Let the scenario 'If the vehicle is powered ON and if power is available to the avionics package, then communication to the vehicle will be established' be represented with statements
$p=$ power is available to avionics package;
$q=$ vehicle is powered ON;
$r=$ communication to the vehicle will be established
The logic form $(p\wedge q)\rightarrow r$ is equivalent to
- A. $\neg r\rightarrow(p\wedge q)$
- B. $p\rightarrow(q\wedge r)$
- C. $\neg p\vee\neg q\vee r$
- D. None of the above
Answer: C. $\neg p\vee\neg q\vee r$
Explanation: The material implication $A \rightarrow B$ is logically equivalent to $\neg A \vee B$.
Applying this to the given expression $(p \wedge q) \rightarrow r$:
$(p \wedge q) \rightarrow r \equiv \neg(p \wedge q) \vee r$.
Using De Morgan's Law on $\neg(p \wedge q)$ yields $\neg p \vee \neg q$.
Substituting this back gives the equivalent expression: $\neg p \vee \neg q \vee r$.