(Fourth Edition of Text)

**Additional Exercise 1:** Consider and . Show that if then *f* is one-to-one and *g*
is onto. Conclude that if and then *f* is a one-to-one correspondence and .

**Additional Exercise 2:** Let *f*:*A* --> *B* with
*A* and *B* finite sets with the same cardinality. Prove that *f* is
one-to-one if and only if *f* is onto.

**Additional Exercise 3:** Show that having the same cardinality is an
equivalence relation.

**Exercises from Section 1.7:** 3, 14, 17, 20, 21, 31, 32, 35, 37,
39, 41, 42

**Exercises from Section 1.8:** 1, 2, 9, 12, 17, 18, 21, 24, 25, 28, 32, 51, 53, 60

**Exercises from Section 2.1:** 7, 9, 11, 12, 13, 17, 18, 19, 23,
25, 26

**Exercises from Section 2.2:** 5, 7, 8, 9, 17, 19

**Exercises from Section 2.3:** 5, 6, 9, 11, 12, 19, 21, 26, 29,
30, 31, 32, 34, 35, 36, 37

**Exercises from Section 2.4:** 1, 2, 3, 4, 14, 15

**Exercises from Section 2.5:** 1, 3, 5, 6, 10, 11, 12, 21, 27, 28

**Exercises from Section 3.2:** 1, 2, 5, 13, 15, 18, 21, 22, 25,
41, 47

**Exercises from Section 3.3:** 1, 2, 26, 27, 31, 32

**Exercises from Section 3.4:** 4, 6, 7, 10, 11, 14, 15, 16, 17

**
**

**Exercises from Section 4.1:** 1, 3, 10, 11, 12, 18, 21, 26, 31, 33, 37, 39, 44, 49, 51

**Exercises from Section 4.2:** 6, 7, 8, 9, 12, 13, 16, 20, 23, 28, 31

**Exercises from Section 4.3:** 9, 11, 13, 15, 17, 25, 26, 27, 47

**Exercises from Section 4.6:** 3, 5, 9, 11, 15, 17, 21, 22, 25, 27, 35, 40, 41

**Exercises from Section 5.1:** 3, 5abc, 7, 9, 13, 17, 18, 19, 21,
26, 29, 30, 34

**Exercises from Section 5.2:** 1, 3, 7, 8, 13, 17, 23

**Exercises from Section 5.4:** 1, 2, 7, 13, 16, 19, 22, 23, 33,
34, 35

**Exercises from Section 8.1:** 2, 13, 14, 21, 22, 23, 24, 32

**Exercises from Section 8.3:** 10, 11, 12, 30, 32

**Exercises from Section 8.4:** 5, 6, 7, 8, 11, 15, 18

Elias Brettler Last modified: Sun Nov 28 17:12:32 EST 1999