Question

What will be relation between two sets of cardinality 3 when the cardinality of their;
union is maximum b. union is minimum c. intersection is minimum d. intersection is maximum​

Answer 1

Given: Two sets each with cardinality 3.

To find: Relation between two sets:

a. Union is maximum: The two sets will be disjoint. i.e. they will have no element in common.

Consider 2 sets:

A = {2, 4, 6}    // Cardinality i.e. number of elements = 3

B = {1, 3, 5}    // Cardinality i.e. number of elements = 3

The two sets are disjoint.

A $\cup$ B = {1,2,3,4,5,6}  //Cardinality is maximum i.e.  6( = 3+3)

b. Union is minimum: The two sets will be identical or equal i.e. all the elements will be same.

Consider 2 sets:

A = {1, 2, 3}    // Cardinality i.e. number of elements = 3

B = {1, 2, 3}    // Cardinality i.e. number of elements = 3

The two sets are equal or identical to each other.

A $\cup$ B = {1,2,3}  //Cardinality is minimum i.e. 3

c. Intersection is minimum: The two sets will be disjoint. i.e. they will have no element in common.

Consider 2 sets:

A = {2, 4, 6}    // Cardinality i.e. number of elements = 3

B = {1, 3, 5}    // Cardinality i.e. number of elements = 3

The two sets are disjoint so no element is common.

A $\cap$ B = {∅}  

d. Intersection is maximum: The two sets will be identical or equal i.e. all the elements will be same.

Consider 2 sets:

A = {1, 2, 3}    // Cardinality i.e. number of elements = 3

B = {1, 2, 3}    // Cardinality i.e. number of elements = 3

The two sets are equal or identical to each other.

A $\cap$ B = {1,2,3}  //Cardinality is  3