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Set theory - Exercise set 1

This exercise set contains some solved exercises on set theory. The theory needed to solve these exercises is introduced in the lecture entitled Set theory.

Exercise 1.1

Define the following sets [eq1]Find the following union:[eq2]

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The union can be written as:[eq3]The union of the three sets $A_{2}$, $A_{3}$ and $A_{4}$ is the set of all elements that belong to at least one of them:[eq4]

Exercise 1.2

Given the sets defined in the previous exercise, find the following intersection:[eq5]

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The intersection can be written as:[eq6]The intersection of the four sets $A_{1}$, $A_{2}$, $A_{3}$ and $A_{4}$ is the set of elements that are members of all the four sets:[eq7]

Exercise 1.3

Suppose that A and $B$ are two subsets of a universal set Omega and that:[eq8]Find the following union:[eq9]

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Using De Morgan's laws:[eq10]

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