Use the Venn diagram to answer the following questions

i. List U, G and H

ii. Find G’, H’, G’ ∩ H’, n(G ∪ H)’ and n(G ∩ H)’

i. From the Venn diagram we get,

U = {1, 2, 3, 4, 5, 6, 8, 9, 10}

G = {1, 2, 4, 8}

H = {2, 6, 8, 10}

ii. U = {1, 2, 3, 4, 5, 6, 8, 9, 10}

G = {1, 2, 4, 8}

H = {2, 6, 8, 10}

∴ G’ = {3, 5, 6, 9, 10} [elements that are present in U but not in G]

∴ H’ = {1, 3, 4, 5, 9} [elements that are present in U but not in H]

∴ G’ ∩ H’ = {3, 5, 9} [elements that are present in both G’ and H’]

∴ G ∪ H = {1, 2, 4, 6, 8, 10} [elements that are present either in G or in H]

∴ (G ∪ H)’ = {3, 5, 9} [elements present in U but not in (G ∪ H)]

∴ n(G ∪ H)’ = 3 [no. of elements in (G ∪ H)’]

∴ G ∩ H = {2, 8} [elements present in both G and H]

∴ (G ∩ H)’ = {1, 3, 4, 5, 6, 9, 10} [elements present in U but not in (G ∩ H)]

∴ n(G ∩ H)’ = 7 [no. of elements in (G ∩ H)’]