Textbook Question
Multiply or divide as indicated. Write answers in lowest terms as needed. (21/8)∙(4/7)
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0. Review of Algebra
Exponents
0:59 minutesProblem 34
Textbook Question
Find the union of the sets. {e,m,p,t,y} ∪ ∅
Verified step by step guidance1
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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Video duration:
59sKey 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}.
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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.
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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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