Discrete Mathematics Answers

Premises: If there was an Easter Concert at the National Arena, then parking was difficult. If they arrived on time, then parking was not difficult. They arrived on time.

Conclusion: There was no Easter Concert.

Determine whether the conclusion follows logically from the premises. Explain by representing the statements symbolically and using rules of inference.

Let proposition p be T and proposition q be F. Find the truth value of the following.

1. p ^ (¬p v q)

2. ¬p v p→q

3. p v ¬q→q

4. p→q↔p

p ^¬q (q→¬p)

Translate the gaming system requirement, , into English where the predicate S(x,y) is “x is in state y” and where the domain for x and y consists of all systems and all possible states, respectively.

What standard form of valid arguments is illustrated with the argument "If it is bright and sunny today, then I will wear my sunglasses. I will not wear my sunglasses. Therefore, it is not bright and sunny today."?

What standard form of valid arguments is illustrated with the argument "If it is bright and sunny today, then I will wear my sunglasses. I will not wear my sunglasses. Therefore, it is not bright and sunny today."?

Express this gaming system requirement using predicates, quantifiers, and logical connectives: “When there are less than 2 gigabytes of available RAM, an error message is displayed.”

Let x, y ∈ R. Determine the truth value of the following statements. Give 5 an example, if true; give a counterexample, if false.