189-235A: Algebra 1

Assignment 2

Weeks of Sept 14-18

1. Using only the principle of induction and the inductive definition of addition given in class, show that addition is associative and commutative.

2. Using only the principle of induction, the inductive definition of multiplication, and the properties of addition established in question 1, show that multiplication is associative and commutative.

3. Using what you have shown in questions 1 and 2, prove by induction the distributive law of multiplication over addition.

4. exercise (3) on page 42 of the notes.

5. Exercise (9) on page 42 of the notes.

6. Exercise (10) on page 42 of the notes.

7. Exercise (13) on page 42 of the notes.

8. Exercise (14) on page 42 of the notes.

9. Exercise (17) on page 42 of the notes.

10. Exercise (19) on page 43 of the notes.