Answer to Question #302386 in Discrete Mathematics for John

Question

Consider the following sets.

U = { 1, 2, …. 10 }

A = { 3, 4, 5, 6, 8, 10 } ` C = { 2, 4, 6, 7, 8 }

B = { 1, 3, 5 }

Perform the following set operations by writing the resulting sets using the roster method. Moreover, sketch the Venn diagram.

1. A’ = ________________________________________________

2.B’ = ________________________________________________

3. A U B = _____________________________________________

4. A ∩ B = _____________________________________________

5. A' ∩ B = _____________________________________________

6. (A ∩ B) U C = _________________________________________

7. A ∩ (B U C’) = _________________________________________

Answer 1

1. $A' = \{1,2,7,9\}$

2. $B' = \{2,4,6,7,8,9,10\}$

3. $A \cup B = \{1,3,4,5,6,8,10\}$

4. $A \cap B = \{3,5\}$

5. $A'\cap B = \{1\}$

6. $(A\cap B)\cup C = \{2,3,4,5,6,7,8\}$

7. $A \cap (B\cup C') = \{3,5,10\}$