Question

Consider statements p and q.p: It is raining.q: Bob is wearing a hat.For parts (a) and (b), fill in the symbolic form. For part (c), choose the descriptive form.

Answer 1

The p and q statements are provided on the problem.

For part (a), it says that it is raining or Bob is wearing a hat. As you can see, it is a combination of the two statements with or as the combining premise. If or is used to establish a relationship between two statements, the correct symbol to be used is v. Hence,

Descriptive form: It is raining or Bob is wearing a hat.

Symbol form: q v p

For part (b), it negates statement p. The correct symbol to represent the descriptive form since it is a negation is ~. Hence, we have

Descriptive form: It is not raining

Symbol form: ~p

For part (c), the relationship Λ stands for and. The symbolic form says that p Λ q. Hence, the descriptive form for this is

Descriptive form: It is raining and Bob is wearing a hat.