There are 10 elements in set A , 7 elements in set B and 14 elements in set A ∪ B . Are the sets A and B disjoint or overlapping? Also, find n ( A ∩ B ) .

Given, Number of elements in the set A = n ( A ) = 10 Number of elements in the set B = n ( B ) = 7 Number of elements in the set A ∪ B = n ( A ∪ B ) = 14 Two sets are said to be disjoint sets, if they have no element in common. Two sets A and B are said to be overlapping, if they contain at least one element in common. In the given sets the number of elements is less than the total number of distinct elements. Hence, the given sets A and B are overlapping sets. Now, we need to find, n ( A ∩ B ) . We know that, n ( A ∪ B ) = n A + n B - n ( A ∩ B ) ⇒ 14 = 10 + 7 - n ( A ∩ B ) ⇒ n ( A ∩ B ) = 17 - 14 ⇒ n ( A ∩ B ) = 3 Therefore, the required answer is 3 .

There are 10 elements in set A , 7 elements in set B and 14 elements in set A ∪ B . Are the sets A and B disjoint or overlapping? Also, find n ( A ∩ B ) .

Given, Number of elements in the set A = n ( A ) = 10 Number of elements in the set B = n ( B ) = 7 Number of elements in the set A ∪ B = n ( A ∪ B ) = 14 Two sets are said to be disjoint sets, if they have no element in common. Two sets A and B are said to be overlapping, if they contain at least one element in common. In the given sets the number of elements is less than the total number of distinct elements. Hence, the given sets A and B are overlapping sets. Now, we need to find, n ( A ∩ B ) . We know that, n ( A ∪ B ) = n A + n B - n ( A ∩ B ) ⇒ 14 = 10 + 7 - n ( A ∩ B ) ⇒ n ( A ∩ B ) = 17 - 14 ⇒ n ( A ∩ B ) = 3 Therefore, the required answer is 3 .

List the members of set A ∩ B from the given Venn diagram.

We have, Here, sets A and B are overlapping sets. We know that, Intersection of any two sets A and B is the set containing all the elements which are common to both sets A and B . So, from the given Venn diagram, elements of A ∩ B can be listed as, A ∩ B = c , j Hence, the required answer is c , j .

List the members of set A ∪ B from the given Venn diagram.

We have, Here, sets A and B are overlapping sets. Union of any two sets A and B is the set of all elements present either in A or B or in both sets A and B . Therefore, elements of A ∪ B can be listed as, A ∪ B = a , c , e , i , j , f , d , g , h Hence, the required answer is a , c , e , i , j , f , d , g , h .

List the members of set A ∪ B ' from the given Venn diagram.

We have, Here, sets A and B are overlapping sets. We know that, The complement of a set A ∪ B is the set containing all the of universal set U , which are not in A ∪ B . So, the elements of A ∪ B ' can be listed as, A ∪ B ' = b , l , m , n , k , o Hence, the required answer is b , l , m , n , k , o .