The union of two sets P and Q is represented by P ∪ Q. This is the set of all different elements that are included in P or Q. The symbol used to represent the union of set is ∪. ... We can say that the intersection of two given sets i.e. P and Q is the set that includes all the elements that are common to both P and Q.
Step-by-step explanation:
Find the Union, Intersection, Relative Complement, and Complement of Sets
In This Article
Set theory has four important operations: union, intersection, relative complement, and complement. These operations let you compare sets to determine how they relate to each other.
Union: Combine elements
The union of two sets is the set of their combined elements. For example, the union of {1, 2} and {3, 4} is {1, 2, 3, 4}. The symbol for this operation is , so
{1, 2} {3, 4} = {1, 2, 3, 4}
Similarly, here’s how to find the union of P and Q:
P Q = {1, 7} {4, 5, 6} = {1, 4, 5, 6, 7}
When two sets have one or more elements in common, these elements appear only once in their union set. For example, consider the union of Q and R. In this case, the elements 4 and 6 are in both sets, but each of these numbers appears once in their union:
Similarly, the union of any set with an empty set, , is itself:
P = P
Intersection: Find common elements
The intersection of two sets is the set of their common elements (the elements that appear in both sets). For example, the intersection of {1, 2, 3} and {2, 3, 4} is {2, 3}. The symbol for this operation is . You can write the following:
{1, 2, 3} {2, 3, 4} = {2, 3}
Similarly, here’s how to write the intersection of Q and R:
Q R = {4, 5, 6} {2, 4, 6, 8, 10} = {4, 6}
When two sets have no elements in common, their intersection is the empty set ():
P Q = {1, 7} {4, 5, 6} =
The intersection of any set with itself is itself:
P P = P
But the intersection of any set with is :
P =
Relative complement: Subtract elements
The relative complement of two sets is an operation similar to subtraction. The symbol for this operation is the minus sign (–). Starting with the first set, you remove every element that appears in the second set to arrive at their relative complement. For example,
{1, 2, 3, 4, 5} – {1, 2, 5} = {3, 4}
Similarly, here’s how to find the relative complement of R and Q. Both sets share a 4 and a 6, so you have to remove those elements from R:
R – Q = {2, 4, 6, 8, 10} – {4, 5, 6} = {2, 8, 10}
Note that the reversal of this operation gives you a different result. This time, you remove the shared 4 and 6 from Q:
Answers & Comments
Answer:
The union of two sets P and Q is represented by P ∪ Q. This is the set of all different elements that are included in P or Q. The symbol used to represent the union of set is ∪. ... We can say that the intersection of two given sets i.e. P and Q is the set that includes all the elements that are common to both P and Q.
Step-by-step explanation:
Find the Union, Intersection, Relative Complement, and Complement of Sets
In This Article
Set theory has four important operations: union, intersection, relative complement, and complement. These operations let you compare sets to determine how they relate to each other.
Union: Combine elements
The union of two sets is the set of their combined elements. For example, the union of {1, 2} and {3, 4} is {1, 2, 3, 4}. The symbol for this operation is , so
{1, 2} {3, 4} = {1, 2, 3, 4}
Similarly, here’s how to find the union of P and Q:
P Q = {1, 7} {4, 5, 6} = {1, 4, 5, 6, 7}
When two sets have one or more elements in common, these elements appear only once in their union set. For example, consider the union of Q and R. In this case, the elements 4 and 6 are in both sets, but each of these numbers appears once in their union:
Q R = {4, 5, 6} {2, 4, 6, 8, 10} = {2, 4, 5, 6, 8, 10}
The union of any set with itself is itself:
P P = P
Similarly, the union of any set with an empty set, , is itself:
P = P
Intersection: Find common elements
The intersection of two sets is the set of their common elements (the elements that appear in both sets). For example, the intersection of {1, 2, 3} and {2, 3, 4} is {2, 3}. The symbol for this operation is . You can write the following:
{1, 2, 3} {2, 3, 4} = {2, 3}
Similarly, here’s how to write the intersection of Q and R:
Q R = {4, 5, 6} {2, 4, 6, 8, 10} = {4, 6}
When two sets have no elements in common, their intersection is the empty set ():
P Q = {1, 7} {4, 5, 6} =
The intersection of any set with itself is itself:
P P = P
But the intersection of any set with is :
P =
Relative complement: Subtract elements
The relative complement of two sets is an operation similar to subtraction. The symbol for this operation is the minus sign (–). Starting with the first set, you remove every element that appears in the second set to arrive at their relative complement. For example,
{1, 2, 3, 4, 5} – {1, 2, 5} = {3, 4}
Similarly, here’s how to find the relative complement of R and Q. Both sets share a 4 and a 6, so you have to remove those elements from R:
R – Q = {2, 4, 6, 8, 10} – {4, 5, 6} = {2, 8, 10}
Note that the reversal of this operation gives you a different result. This time, you remove the shared 4 and 6 from Q:
Q – R = {4, 5, 6} – {2, 4, 6, 8, 10} = {5}