MATH1081 Discrete Mathematics UNSW Sydney
Board Tutorial Week 2
Topic 1 – Set theory (continued).
Venn diagrams; set operations; laws of set algebra; Cartesian product.
Exercises
1. For each set expression below involving sets A, B, and C, draw up a Venn diagram and shade
its corresponding regions.
(a) (A ∩ B) ∪ C.
(b) (A − B) ∪ (A − C).
(c) (A ⊖ B) ⊖ C.
2. Write set expressions for the shaded regions in each of the following Venn diagrams.
(a) U (c) U
A B A B
C C
(b) U (d) U
A B A B
C C
3. Suppose that A, B, and C are sets and that A ⊆ B c ∪ C. Decide whether each of the following
statements is true or false, and prove your answer in each case.
(a) A ∩ B = ∅.
(b) A ∩ B ⊆ C.
Board Tutorial Week 2
Topic 1 – Set theory (continued).
Venn diagrams; set operations; laws of set algebra; Cartesian product.
Exercises
1. For each set expression below involving sets A, B, and C, draw up a Venn diagram and shade
its corresponding regions.
(a) (A ∩ B) ∪ C.
(b) (A − B) ∪ (A − C).
(c) (A ⊖ B) ⊖ C.
2. Write set expressions for the shaded regions in each of the following Venn diagrams.
(a) U (c) U
A B A B
C C
(b) U (d) U
A B A B
C C
3. Suppose that A, B, and C are sets and that A ⊆ B c ∪ C. Decide whether each of the following
statements is true or false, and prove your answer in each case.
(a) A ∩ B = ∅.
(b) A ∩ B ⊆ C.
