Question

Symbolize the following sentences in SL using the symbolization key provided:

A: Aaron is in the office.
B: Bryan is in the office.
J: Jerry goes home early.
S: It's sunny.
T: It's Tuesday.
W: It's warm.

a. It's not both sunny and warm.
b. Aaron or Bryan is in the office.
c. Aaron is in the office if Bryan is.
d. Bryan is in the office only if it's Tuesday.
e. It's Tuesday, and although it's sunny, it's not warm.
f. It's neither sunny nor warm, but Jerry still went home early.
g. Aaron is in the office or Jerry went home early, but not both.
h. Bryan is in the office if and only if it's Tuesday and it isn't warm.
i. Jerry will go home early unless Aaron is in the office or it's not sunny.
j. If neither Aaron nor Bryan is in the office, then if it's sunny and warm, it must be Tuesday.

Answer 1

To symbolize sentences in Sentential Logic, logical connectors and provided symbols are used to represent the structure of each given statement.

Step-by-step explanation:

To symbolize the given sentences in Sentential Logic (SL) using the provided key, follow these steps for each:

• a. It's not both sunny and warm: ¬(S ∧ W).
• b. Aaron or Bryan is in the office: A ∨ B.
• c. Aaron is in the office if Bryan is: B → A.
• d. Bryan is in the office only if it's Tuesday: T → B.
• e. It's Tuesday, and although it's sunny, it's not warm: T ∧ (S ∧ ¬W).
• f. It's neither sunny nor warm, but Jerry still went home early: ¬S ∧ ¬W ∧ J.
• g. Aaron is in the office or Jerry went home early, but not both: (A ∨ J) ∧ ¬(A ∧ J).
• h. Bryan is in the office if and only if it's Tuesday and it isn't warm: (T ∧ ¬W) ↔ B.
• i. Jerry will go home early unless Aaron is in the office or it's not sunny: ¬(A ∨ ¬S) → J.
• j. If neither Aaron nor Bryan is in the office, then if it's sunny and warm, it must be Tuesday: ¬(A ∨ B) → (S ∧ W → T).

These symbolizations use logical connectors to represent the structure of each sentence precisely.