MATH1081_board_tutorial_Week_2___SHORT_ANSWERS.

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.