Question

U = {1, 2, 3, 7, 8, 9, 10, 11, 12} P = {1, 3, 7,10}, then 

i. show the sets U, P and P’ by Venn diagram. 

ii. Verify (P’)’ = P

Answer 1

i. Here, U = {1,2, 3, 7, 8,9, 10, 11, 12} P = {1, 3, 7, 10} 

∴ P’ = {2, 8, 9, 11, 12}

ii. Here, U = {1, 2, 3, 7, 8, 9, 10, 11, 12} 

P = {1, 3, 7, 10} ….(i) 

∴ P’ = {2, 8, 9, 11, 12} 

Also, (P’)’ = {1,3,7, 10} …(ii) 

∴ (P’)’ = P … [From (i) and (ii)]