Theory question 101
Sets(a) If A = {multiples of 2}, B = {multiples of 3} and C = {factors of 6} are subsets of μ = {x : 1 ≤ x ≤ 10}, find A′ ∩ B′ ∩ C′.
(b) Tickets for a movie premiere cost $18.50 each while the bulk purchase price for 5 tickets is $80.00. If 4 gentlemen decide to get a fifth person to join them so that they can share the bulk purchase price equally, how much would each person save?
Show the model answer
Model answer
(a) A = {2, 4, 6, 8, 10}, B = {3, 6, 9}, C = {1, 2, 3, 6}
A′ = {1, 3, 5, 7, 9}, B′ = {1, 2, 4, 5, 7, 8, 10}, C′ = {4, 5, 7, 8, 9, 10}
A′ ∩ B′ ∩ C′ = {5, 7}
(b) Bulk share = $80 ÷ 5 = $16 each
Saving per person = $18.50 − $16.00 = $2.50
Explanation
List μ first, then each complement; only elements in all three complements remain.