Question

Example 1:

Let P, Q and R be the propositions

P: It’s raining outside.

Q: It’s safe to drive.

R: The roads are slippery.

 

a)      Though it’s raining outside but the roads are not slippery.

b)     It’s safe to drive if and only if the roads are not slippery:

  

c)      If it’s raining outside and the roads are not slippery then it’s safe to drive.

d)     Driving is safe after the rain stopped if and only if the roads are not slippery.

Answer 1

a)   In the symbolic form "Though it’s raining outside but the roads are not slippery." is $P\land \neg R.$

b)   In the symbolic form "It’s safe to drive if and only if the roads are not slippery." is $Q\leftrightarrow\neg R.$

c)   In the symbolic form "If it’s raining outside and the roads are not slippery then it’s safe to drive." is $P\land \neg R\rightarrow Q.$

d)  In the symbolic form "Driving is safe after the rain stopped if and only if the roads are not slippery." is $\neg P\land Q\leftrightarrow\neg R.$