COS1501 Assignment 2 2024 (653506) - 14 June 2024

COS1501 Assignment 2
2024 (653506) - 14 June
2024
COMPLETE ANSWERS




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, COS1501 Assignment 2 2024 (653506) - 14 June 2024

Question 1: Venn Diagram for [(A ⋂ B)' - C] ⋂ [(A + B) - C]

To solve this, let's break down the expression step by step and draw the Venn diagrams
accordingly:

1. [(A ⋂ B)' - C]:

o First, find the complement of A∩BA \cap BA∩B: This is everything outside
A∩BA \cap BA∩B.

o Subtract CCC from this complement.

2. [(A + B) - C]:

o Find A+BA + BA+B, which is A∪BA \cup BA∪B.

o Subtract CCC from A∪BA \cup BA∪B.

Combining these two results using intersection gives us the desired set.

Since I don't have the Venn diagrams to choose from (options a, b, c, d), you would need to refer
to those to identify which diagram correctly represents the set.

Question 2: Counterexample for (A - B) U C' = (C' - B) + A

To find a counterexample:

• Substitute each given set of A,B,A, B,A,B, and CCC into both sides of the equation.

• Check if both sides are equal for any given set. If they are not equal for one set, that set is
a valid counterexample.

Let's go through the options:

• Option a: A = {1}, B = {2}, C = {3}

• Option b: A = {1}, B = {1}, C = {2}

• Option c: A = {1, 2}, B = {1, 2}, C = {3}