Class 11th Maths Textbook Chapter 1: Sets Exercise 5: Complement of a Set Question 4 (ii) Solution

Question

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}, verify that: (ii) (A $\cap$ B)' = A' $\cup$ B'

Accepted Answer

Find the intersection of sets A and B by finding all common elements from both sets.
 	ext{A $\cap$ B = \{2\}} Find the complement of set (A $\cap$ B) by finding the elements of set U that are not elements of set (A $\cap$ B).
 	ext{(A $\cap$ B)' = \{1, 3, 4, 5, 6, 7, 8, 9\}} Find the complement of set A by finding the elements of set U that are not elements of set A.
 	ext{A' = \{1, 3, 5, 7, 9\}} Find the complement of set B by finding the elements of set U that are not elements of set B.
 	ext{B' = \{1, 4, 6, 8, 9\}} Find the union of sets A' and B' by finding all distinct elements from both sets.
 	ext{A' $\cup$ B' = \{1, 3, 4, 5, 6, 7, 8, 9\}} Determine whether sets (A $\cap$ B)' and (A' $\cup$ B') contain the same elements.
 {green}	extbf{Answer: (A $\cap$ B)' = A' $\cup$ B'}|||	extbf{Reason: Both sets are equal to \{1, 3, 4, 5, 6, 7, 8, 9\}}{/green}

Question: 4 (ii)

Answer