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Answer:
The correct answer to this question is OPTION C.
Step-by-step explanation:
Set Operations
In Set theory, it is very common to see two or more two sets showing some or the other type of relation. Sets can have data common among them which is most likely to happen, sets sometimes do not have any data common, they are known as mutually independent sets. Let’s look at certain operations based on the relationship among sets,
Union of a Set
Union of a set is defined as the set containing all the elements present in set A OR set B. The word “OR” is used to represent the union of a set, which means if the data exists in either A Or B, it will be a part of the Union of the set. The symbol used to denote the Union of a Set is “∪”. The standard definition can be written as, if x ∈ A ∪ B, then x ∈ A or x ∈ B. The Venn diagram for A ∪ B is,
Properties:
A∪ B= B ∪ A [Commutative property]
(A ∪ B) ∪ C= A ∪ (B ∪ C) [Associative property]
A ∪ ∅= A
A ∪ U= U
A good practical example of a Union of two sets can be two friends inviting their other friends to a party, now there is a high possibility that there are friends who are common between them, now there is no point in inviting them twice, hence, the common friends are only invited once and the rest of the friends are also invited, this is what union of a set of friends will look like.
The intersection of a Set
The intersection of a set is defined as the set containing all the elements present in set A and set B. The word “AND” is used to represent the intersection of the sets, it means that the elements in the intersection are present in both A and B. The symbol used to denote the Intersection of the set is “∩”. The standard definition can be written as, if x ∈ A ∩ B, then x ∈ A and x ∈ B. The Venn diagram for A ∩ B is,
Using the above properties in option c we can say b union c has 3 elements [1,3];
Thus a union b and union c have 5 elements [-2,5].
Properties
A∩ B= B∩ A [Commutative property]
(A∩ B) ∩ C= A∩ (B ∩ C) [Associative property]
A∩ U= A
A∩ ∅= ∅
A good practical example of the intersection of two sets can be this, imagine two friends are throwing a party, and they decided to invite only those friends who are their mutual friends of them. They wrote down the names of their friends and then saw the friends which are common and invited only those, this can be called the Intersection of the set of friends.
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