Answer to Question #104695 in Discrete Mathematics for Martin

Question

QUESTION 3

Consider the arguments below and decide whether they are valid. If they are, write down an informal proof, phrased in complete, well-formed English sentences. If the argument is invalid, construct a counter example.

In Questions 3.1 and 3.3 we assume we deal with the blocks language.

Question 3.1

| x or y is at home but either v or z is unhappy
| Either x is not home or z is happy.
| Either y is not home or z is unhappy
|---
| z is unhappy


Question 3.2

| Aggie or Cecil is not shopping.
| Cecil is shopping or Cecil and Aggie are married.
| Aggie and Cecil are not married or Aggie is shopping.
|----
| Cecil and Aggie are married.


Question 3.3

| Student(peter) ∨ Hungry(peter, 2:00)
| ¬ Hungry(peter, 2:00) ∨ ¬Pet(patience)
| Pet(patience) ∨ ¬ Student(peter)
|----
| Student(peter)

Answer 1

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