Find union of the following pair of sets: A = x : x ∈ N and 2 < x ≤ 7 and B = x : x ∈ N and 7 < x ≤ 11 .

We know that, The union of two sets A and B is defined as the set of all the elements which lie in set A and set B or both the elements in A and B altogether. The union of the set is denoted by the symbol ' ∪ ' . Example: X = 1 , 2 , 3 , Y = 2 , 4 X ∪ Y = 1 , 2 , 3 , 4 Now, the given sets are, A = x : x ∈ N and 2 < x ≤ 7 = 3 , 4 , 5 , 6 , 7 B = x : x ∈ N and 7 < x ≤ 11 = 8 , 9 , 10 , 11 So, A ∪ B = 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 = x : x ∈ N and 3 ≤ x ≤ 11

Find union of the following pair of sets: A = x : x is an integer ≤ 6 and B = x : x is an integer ≥ 4 .

We know that, The union of two sets A and B is defined as the set of all the elements which lie in set A and set B or both the elements in A and B altogether. The union of the set is denoted by the symbol ' ∪ ' . Example: X = 1 , 2 , 3 , Y = 2 , 4 X ∪ Y = 1 , 2 , 3 , 4 Now, the given sets are, A = x : x is an integer ≤ 6 = . . . , - 1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 B = x : x is an integer ≥ 4 = 4 , 5 , 6 , 7 , . . . So, A ∪ B = . . . , - 1 , 0 , 1 , 2 , 3 , 4 , . . . = x : x is an integer

Let A = a , b , i and B = a , i , b , c . Is A ⊂ B ? What is A ∪ B ? Prove that A ∩ B = A and A ∪ B = B .

A set P is a subset of another set Q if all elements of the set P are elements of the set Q . In other words, P ⊂ Q if whenever a ∈ P , then a ∈ Q . Given, A = a , b , i and B = a , i , b , c Clearly, A ⊂ B as each element of A is also an element of B . The union of two sets A and B is defined as the set of all the elements which lie in set A and set B or both the elements in A and B altogether. So, A ∪ B = a , b , c , i = B The intersection of two sets A and B is the set of all those elements which are common to both A and B . So, A ∩ B = a , b , i = A

Find the intersection for the following pair of sets. A = x : x ∈ N and 2 < x ⩽ 7 and B = x : x ∈ N and 7 < x ⩽ 11 .

Given sets are, A = x : x ∈ N and 2 < x ⩽ 7 and B = x : x ∈ N and 7 < x ⩽ 11 . We know that, The intersection of sets A and B is the set of all elements which are common to both A and B . The symbol ' ∩ ' is used to represent intersection. So, A ∩ B = x : x ∈ A and x ∈ B A = x : x ∈ N and 2 < x ⩽ 7 = 3 , 4 , 5 , 6 , 7 B = x : x ∈ N and 7 < x ⩽ 11 = 8 , 9 , 10 , 11 A ∩ B = ϕ The intersection of two sets is a set of common elements of both sets. Therefore, A ∩ B = ϕ .