Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 34

Chapter 1, Problem 34

Find the union of the sets. {e,m,p,t,y} ∪ ∅

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Identify the two sets involved in the union operation: the first set is $\{e, m, p, t, y\}$ and the second set is the empty set $\emptyset$.

Recall the definition of union of two sets: the union $A \cup B$ is the set containing all elements that are in $A$, or in $B$, or in both.

Since the second set is the empty set $\emptyset$, it contains no elements to add to the union.

Therefore, the union $\{e, m, p, t, y\} \cup \emptyset$ will contain exactly the elements of the first set.

Write the union result as $\{e, m, p, t, y\}$, which is the same as the first set.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Union

The union of two sets combines all unique elements from both sets into one set. It is denoted by the symbol ∪. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.

Empty Set (∅)

The empty set, denoted by ∅, is a set that contains no elements. It is a subset of every set, and when combined with another set using union, it does not add any new elements.

Properties of Set Operations

Set operations follow specific properties such as identity and idempotent laws. For union, the identity property states that the union of any set with the empty set is the set itself, meaning A ∪ ∅ = A.

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