Part 1 Logic and Proof Identify if the following are propositions. If the statement is not proposition write as "Not a proposition since it is a command statement. "Then, write their representation if it is a proposition. (5 points Each)
1. I will study discrete math or I will study English literature.
2. If it is snowing, then I will study discrete math. 3. I will study discrete math and English literature 4. If Jimmy is wealthy and not boring, then he is a friend of mine.
1. I will study discrete math or I will study English literature.
2. If it is snowing, then I will study discrete math. 3. I will study discrete math and English literature 4. If Jimmy is wealthy and not boring, then he is a friend of mine.
Answers & Comments
Answer:
1. The statement "I will study discrete math or I will study English literature" is a proposition. It can be represented as p ∨ q, where p represents "I will study discrete math" and q represents "I will study English literature."
2. The statement "If it is snowing, then I will study discrete math" is a proposition. It can be represented as r → p, where r represents "It is snowing" and p represents "I will study discrete math."
3. The statement "I will study discrete math and English literature" is not a proposition since it is a command statement.
4. The statement "If Jimmy is wealthy and not boring, then he is a friend of mine" is a proposition. It can be represented as s ∧ ¬t → u, where s represents "Jimmy is wealthy," t represents "Jimmy is boring," and u represents "Jimmy is a friend of mine."