Question

Fill in the blanks with elements of that set. 

U = {1, 3, 5, 8, 9, 10, 11, 12, 13, 15} 

A = {1,11, 13} 

B = {8,5, 10, 11, 15} 

A’ = { } 

B’ = { } 

A ∩ B = { } 

A’ ∩ B’ = { } 

A ∪ B = { } 

A’ ∪ B’ = { } 

(A ∩ B)’ = { } 

(A ∪ B)’ = { } 

Verify: (A ∩ B)’ = A’ u B’ , (A u B)’ = A’ ∩ B’

Answer 1

U = {1, 3, 5, 8, 9, 10, 11, 12, 13, 15} 

A = {1, 11, 13} 

B = {8, 5, 10, 11, 15} 

A’ = {3, 5, 8, 9, 10, 12, 15} 

B’ = {1, 3, 9, 12, 13} 

A ∩ B= {11} 

A’ ∩ B’ = {3, 9, 12} …(i) 

A ∪ B = {1, 5, 8, 10, 11, 13, 15} 

A’ ∪ B’ = { 1, 3, 5, 8, 9, 10, 12, 13, 15} … (ii) 

(A ∩ B)’ = { 1, 3, 5, 8, 9, 10, 12, 13,15} … (iii) 

(A ∪ B)’ = {3, 9, 12} ,..(iv) 

(A ∩ B)’ = A’ ∪ B’ … [From (ii) and (iii)]

(A ∪ B)’ = A’ ∩ B’ … [From (i) and (iv)]