Solve any two of the following:

Let U = {1, 2, 3, ..., 10}, A = {2, 4, 6, 8, 10}, B = {1, 3, 5, 7, 9, 10}.
Find:
(i) (A ∪ B)'
(ii) (A ∩ B)'
(iii) B'
(iv) B - A

The complement of the union of sets A and B is empty, i.e., (A ∪ B)' = ∅. The difference between set B and set A, which includes elements in B but not in A, is {1, 3, 5, 7, 9}.
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Answered by Anonymous | 2025-07-04

To solve the given problems, we first need to understand the concepts of union, intersection, complement, and difference of sets. We have the universal set U = { 1 , 2 , 3 , ... , 10 } , set A = { 2 , 4 , 6 , 8 , 10 } , and set B = { 1 , 3 , 5 , 7 , 9 , 10 } .
Let's solve two of the provided options:
(i) ( A ∪ B ) ′

The union A ∪ B is the set of all elements that are in either A or B or in both.

So, A ∪ B = { 2 , 4 , 6 , 8 , 10 } ∪ { 1 , 3 , 5 , 7 , 9 , 10 } = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } .

The complement of this set, ( A ∪ B ) ′ , is the set of elements in U but not in A ∪ B .

Since A ∪ B includes all elements from U , the complement ( A ∪ B ) ′ = ∅ .


(ii) ( A ∩ B ) ′

The intersection A ∩ B is the set of all elements that are both in A and B .

So, A ∩ B = { 10 } , because 10 is the only element that appears in both sets.

The complement of this set, ( A ∩ B ) ′ , is the set of elements in U but not in A ∩ B .

Therefore, ( A ∩ B ) ′ = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } .


In summary, we have solved two options:

( A ∪ B ) ′ = ∅

( A ∩ B ) ′ = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 }

Answered by EmmaGraceJohnson | 2025-07-06