Question

Construct truth-functionsl psrsphrases of the following sentences and symbolsize those paraphrases in SL, using the following symbolization key: P: The Red Sox improve their pitching, G: The Red Sox have a good chance of winning the American League pennant, Y: The Yankees will win the pennant, F: The Red Sox falter, T: The Twins win tonight, M: The Mariners win tonight, A: The Angels win tonight, I: The Indians win tonight, S: The Indians's starting pitcher can go the full nine innings, N: The Angels move into first place, H: The rain stops within an hour, G: the game will be postponed, R: The Royals are in the running for the pennant. h. The Red Sox have a good chance of winning the pennant if and only the Mariners and the Angels and the Twins all lose tonight.

Answer 1

Solution

1) If the Red Sox improve their itching then the Red Sox have a good chance of winning the American League pennant.

2) If (it is not the case that the Twins win tonight and it is not the case that the Mariners win tonight) then the Angels move into first place.

3)If the Indian’s starting pitcher can go the full nine innings then the Indians win tonight.

S ⊃ I

4)If (the Twins win tonight or the Mariners win tonight) then it is not the case that the Royals are in the running for the pennant.

(T ∨ M) ⊃ ~ R

5)(It is not the case that the Royals are in the running for the pennant and the Yankees will win the pennant) if and only if [the Twins win tonight and (it is not the case that the Mariners win tonight and it is not the case that the Angels win tonight)].

(~ R & Y) [T & (~ M & ~ A)]