Let P be the proposition "It is snowing". Let Q be the proposition "I will go to town". Let R be the proposition "I have time".

Let P be the proposition “It is snowing”.

Let Q be the proposition “I will go to town”.

Let R be the proposition “I have time”.

(a) Using logical connectives, write a proposition which symbolizes

each of the following:

(i) If it is not snowing and I have time, then I will go to town.

(ii) I will go to town only if I have time.

(iii) It isn’t snowing.

(iv) It is snowing, and I will not go to town.

(b) Write a sentence in English corresponding to each of the

following propositions:

(i) Q ⇔ ( R ∧ ¬P )

(ii) R ∧ Q

(iii) (Q ⇒ R ) ∧ ( R  ⇒ Q)  

(iv) ¬ ( R ∧ Q)  .