Verify. ( A∪B) '=A' ∩B' using venn diagrams.
Answers
SOLUTION :
Venn diagram :
A Venn diagram is a closed figure used to denote a set. Points within such a closed figure represent the elements of the set. Venn diagrams can be used to represent the relationship between sets. That Universal set U is usually represented by a rectangle. All the elements of a set are indicated by points inside the circle representing the set. The elements can also be written inside the circle without marking the points. An object that is not a member of a set is placed outside the circle representing the set.
•A\B means removing all elements of B from A.
Union of two sets :
The union of the sets A and B is the set of all the element that belongs to either A or B or both. It is denoted by A U B(“A union B”).
Intersection of two sets :
The intersection of the sets a and b is the set of all the elements which belong to both A and B. It is denoted by A ∩ B (“ A intersection B”).
•If A and B do not have any element in common then A ∩ B= a null set = Ø
VENN DIAGRAMS IS ON THE ATTACHMENT.
Hence, (A ∩ B) U (A\B) = A
Answer:
SOLUTION :
Venn diagram :
A Venn diagram is a closed figure used to denote a set. Points within such a closed figure represent the elements of the set. Venn diagrams can be used to represent the relationship between sets. That Universal set U is usually represented by a rectangle. All the elements of a set are indicated by points inside the circle representing the set. The elements can also be written inside the circle without marking the points. An object that is not a member of a set is placed outside the circle representing the set.
•A\B means removing all elements of B from A.
Union of two sets :
The union of the sets A and B is the set of all the element that belongs to either A or B or both. It is denoted by A U B(“A union B”).
Intersection of two sets :
The intersection of the sets a and b is the set of all the elements which belong to both A and B. It is denoted by A ∩ B (“ A intersection B”).
•If A and B do not have any element in common then A ∩ B= a null set = Ø
VENN DIAGRAMS IS ON THE ATTACHMENT.
Hence, (A ∩ B) U (A\B) = A
Step-by-step explanation: