Exercise 7 (Chapter Review)

Consider the statement: $\forall x (\forall y (x + y = y) \imp \forall z (x\cdot z = 0))$.

1. Explain what the statement says in words. Is this statement true? Be sure to state what you are taking the universe of discourse to be.

2. Write the converse of the statement, both in words and in symbols. Is the converse true?

3. Write the contrapositive of the statement, both in words and in symbols. Is the contrapositive true?

4. Write the negation of the statement, both in words and in symbols. Is the negation true?