If 52 people drink juice and 20 people drink milk how

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Unformatted text preview: T c = {x |x ∈ S and x ∈ T c } =? S c ∪ T c =? (S ∩ T )c =? M. Chen (IE@CUHK) ENGG2430 lecture 1 8 / 16 Set Operations – Examples Question #1: 70 drink orders are made in a restaurant, and there are two types of drinks: juice and milk. If 52 people drink juice and 20 people drink milk, how many people drank both milk and juice? Question #2: Three popular computer games are WoW, Delta, and Super Mario. 40 people in your neighborhood own computer games. 6 of them own all three games, 5 own only Delta, 7 own only Super Mario, and 19 own only WoW. How many total computer games are owned in your neighborhood? Question #3: A group of 100 aliens arrive on Starship 2050 to invade our earth. These aliens are characterized by two distinct features, their eyes and their tails. Some aliens have eyes but no tail, some have a tail but no eyes, and some have eyes and a tail. If there are 75 aliens that have eyes, and 50 aliens that have eyes and a tail, how many aliens have eyes but no tail? How many have only a tail but no eyes? M. Chen (IE@CUHK) ENGG2430 lecture 1 9 / 16 Venn Diagram “Venn diagram is a diagram that shows all possible logical relations between a finite collection of sets.” - wiki (Figure 1.1 from the textbook) M. Chen (IE@CUHK) ENGG2430 lecture 1 10 / 16 Algebra of Sets Are the following correct? How to do sanity check? (S c )c = S S ∩ S c = 0, S ∪ S c = Ω / S ∪ Ω = Ω, S ∩ Ω = S S ∩ (T ∪ U ) = (S ∩ T ) ∪ (S ∩ U ) S ∪ (T ∩ U ) = (S ∪ T ) ∩ (S ∪ U ) M. Chen (IE@CUHK) ENGG2430 lecture 1 11 / 16 Exercise Problem 1.2(a) from textbook Let A and B be two sets, show that Ac = (Ac ∩ B ) ∪ (Ac ∩ B c ), B c = (A ∩ B c ) ∪ (Ac ∩ B c ). (LOGIC) Let A and B be two sets. From the following statement, relate A and B : An element x is in set A if it is in...
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