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## Sets and Set Operations

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**Objectives**• Determine if a set is well defined. • Write all the subsets of a given set and label the subsets as proper or improper. • Given a universal set and some subsets, find a complement, intersection or union. • Draw a Venn diagram to illustrate two sets. • Use the cardinal number formula.**Vocabulary**• roster notation • set-builder notation • well defined set • cardinal number • empty set • subset • proper/improper subset • intersection of sets • union of sets • mutually exclusive • complement of a set**Set:**roster notation: set builder notation: well defined set:**Determine if the given set is well defined.**The set of all pink automobiles The set of all good bands The set of odd numbers The set of small numbers**Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2,**4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below: • Find n(B). • Find the set A B. • Find the set B . • Find the set A B.**Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2,**4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below: • Is 7A true or false? • Is 5B true or false?**Formulas**Cardinal Number Formula for the Union of Sets n(AB) = n(A) + n(B) — n(AB) Cardinal Number Formula for the Complement of a Set n(U) = n(A) + n(A )**Suppose n(U) = 61, n(A) = 32, and n(B) = 26.**If n(AB) = 40, find n(AB) and draw a Venn diagram to illustrate the composition of U.**In a recent health survey, 750 single men in their twenties**were asked to check the appropriate box or boxes on the following form. I am a member of a private gym. I am a vegetarian. The results were tabulated as follows: 374 checked the gym box 92 checked the vegetarian box 332 were blank (no boxes checked)**750 men surveyed**374 checked the gym box 92 checked the vegetarian box 332 were blank (no boxes checked) • Draw a Venn diagram illustration the results of the survey. • What percent of these men were both members of a private gym and vegetarians.**Cards**Determine how many cards, in an ordinary deck of 52, are clubs or twos.**Cards**Determine how many cards, in an ordinary deck of 52, are face cards or diamonds.**Cards**Determine how many cards, in an ordinary deck of 52, are threes or sixes.**Cards**Determine how many cards, in an ordinary deck of 52, are threes and sixes.