Question

Identify propositions within each sentence, assign a single-letter variables name for each proposition, provide compound propositions equivalent to each sentence using these variables, and use truth tables to exhaustively explore truth values of these compound propositions.

1. Roses are red and violets are blue.

2. Roses are red and either violets are blue or sugar is sweet

3. Either it will rain or snow, but not both

4. If Jane wins or if Jane loses, then Jane will be tired.

5. If the program halted, then the message was corrupted or the connection was ended.

Answer 1

See attachment and explanation for further details.

Explanation:

A = Roses are red, B = Violets are blue, C = Sugar is sweet, D = It will rain, E = It will snow, F = Jane wins, G = Jane loses, H = Jane will be tired, I = The program halted, J = The message was corrupted, K = The connection was ended.

1) A ∧ B

2) A ∧ (B ∨ C)

3) (D ∨ E) ∧ ¬ (D ∧ E)

4) (F ∨ G) ⇒ H

5) I ⇒ (J ∨ K)

Truth values of each proposition are presented below as attachments.