COS1501 Assignment 2 2024 (653506) - 14 June 2024

+254792947610



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

, 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.