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Let $A$, $B$, $C$ be three sets as shown in the following Venn diagram. For each of the following sets, draw a Venn diagram and shade the area representing the given set.
Given the following sets: U = {1,2,3,4,5,6,7} A= {2,3,4,5} and B = {4,5} and knowing that U is the Universal Set (i.e., the set of all elements under consideration), answer the following questions.
Describe each of the following sets both in words and by listing out enough elements to see the pattern. This is the set of all numbers which are 3 less than a natural number (i.e., that if you add 3 to them, you get a natural number).
Solved examples on Venn diagram are discussed here. From the adjoining Venn diagram, find the following sets.
Use set builder notation to give a description of each of these sets. Find the power set of each of the following sets, where a and b are distinct elements. We have an expert-written solution to …
Determine whether or not the following relations are equivalence relations on the given set. If the relation is an equivalence relation, describe the partition given by it.
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Find the truth set of each of the given predicates if the domain is a set of integers. Let A be the set of students who live within one mile of school and let B be the set of students who walk to …
To prove this, both subset relations A ⊆ B and B ⊆ A must be proved. Suppose x is a particular but arbitrarily chosen element of A. [We must show that x ∈ B. By definition of B, this means we must show that x = 2·(some integer)−2.] By definition of A, there is an integer a such that x = 2a.
This page titled 2.E: Basic Concepts of Sets (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Pamini Thangarajah.
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