Discrete mathematics 314

Please help me solve the following complex questions.

Make sure to thoroughly supplement your answer.

1. Give an example of a tautology where A is any statement.

2. State a complex contradiction statement and explain how you arrived at that point.

3. In what context can you argue out the statement (A A) (q T)?

4. Given the statement A (A (A T), prove whether the statement is true or false.

5. Statement A (A q) can be classified in what category?

6. The following statement is a proposition q p. What proposition is it?

7. The following statement is a true statement (A F) (A T). Prove your answer.

8. What is the name given to a proposition that is neither a contradiction nor a tautology?

9. p q is the inverse of which proposition?

10. p q is the converse of which proposition?