56 CHAPTER 2 Sets Exercises Warm Up Exercises In Exercises 1– 4, fill in the blank with an appropriate word, phrase, or symbol(s). 1. If all the elements of set A are also elements of set B, then set A is a(n) ________ of set B. Subset 2. If all the elements of set A are also elements of set B, and set ≠ A set B, then set A is a(n) ________ subset of set B. Proper 3. The expression for determining the number of distinct subsets for a set with n distinct elements is ________. 2n 4. The expression for determining the number of distinct proper subsets for a set with n distinct elements is ____________. − 2 1 n Practice the Skills In Exercises 5–26, answer true or false. If false, give the reason. 5. {Pikachu, Eevee, Snorlax} {Pikachu, Eevee, Snorlax, Charizard, Garchamp} # True 6. {Pacific} {Atlantic, Pacific, Indian, Artic} # True 7. {apple, pear} {pear, peach, grape, orange} # False; apple is not in the second set. 8. {dog, cat} {dog, bird, hamster} # False; cat is not in the second set. 9. {Elite, Euphoria, Skins} {Atypical, Elite, Euphoria, Riverdale, Skins} , True 10. {American, Southwest} {Delta, American, Southwest} , True 11. {rock, paper, scissors} {rock, paper, scissors} , False; no set is a proper subset of itself. 12. {engineer, social worker, teacher, architect} {social worker, teacher, engineer, architect} , False; no set is a proper subset of itself. m Eevee from Pokémon 13. ∈ book {book, magazine, newspaper} True 14. ∈ necklace {necklace, ring, bracelet, earring} True 15. ∈ {Rouge} {Five, Muse, Paramount, Rouge, Westlife} False; {Rouge} is a set, not an element. 16. ∈ {} {a, b, c, d} False; { } is a set, not an element. 17. ∉ tiger {zebra, giraffe, polar bear} True 18. {} {vanilla, chocolate, strawberry} # True 19. {chair} {sofa, table, chair} , True 20. a b c c b a {, , } {, , } ÷ True 21. = ∅ {} { } False; the set { }∅ contains the element .∅ 22. ∅ = {} True 23. = ∅ {0} False; the set {0} contains the element 0. 24. {} {} # True 25. = 0 {} False; 0 is a number and { } is a set. 26. ∈ {1} {{1}, {2}, {3}} True In Exercises 27–34, determine whether = A B A B B A , , , # # A B B A , , , , or if none of these applies. (There may be more than one answer.) 27. = A {Amp, Monster, Red Bull, Rockstar} = B {Rockstar, Amp, Monster} B A B A , # , 28. = A {2, 4, 6, 8} = B {2, 3, 4, 5, 6, 7, 8} A B A B , # , 29. = | = | A x x B x x { is a citizen of the United States} { is a citizen of the state of Tennessee} B A B A , # , 30. = | = | A x x B x x { is an Olympic sport} { is a sport} A B A B , # , SECTION 2.2 Cfg1978/Shutterstock PCN Black/PCN Photography/Alamy Stock Photo
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