Homework #1-18: Answer yes or no, if no give the reason 1) Is A ⊆ B given A = silver, B = {gold, silver, diamond} A is not a set, so it can’t be a proper subset. Answer: no, because A is not a set 3) Is C ⊆ D given C = {Phoenix}, D = {Phoenix, Glendale, Peoria, Scottsdale} I need two rules to work. C is a set so rule 1 is satisfied. Every element of C is also an element of D, so rule 2 is satisfied. Answer: yes 5) Is A ⊆ B given A = {2,3} , B = {1,2,3,4,5} I need two rules to work. A is a set so rule 1 is satisfied. Every element of A is also an element of B, so rule 2 is satisfied. Answer: yes 7) Is A ⊆ B given A = a, B = {푥|푥 푖푠 푎 푣표푤푒푙} A is not a set, so it can’t be a proper subset. Answer: no, because A is not a set 9) Is A ⊆ B given A = { }, B = {1,2,3,4,5} Answer yes: the empty set is a subset of every set. 11) Is S ⊂ T given, S= ∅, T = {1,2,3,4,5} Answer yes: the empty set is a subset of every set. 13) Is A ⊂ B given A = {1,2,3}, B = {3,2,1} This is not a true statement. The sets are equal and this symbol does not allow sets to be equal. Answer: no, sets are equal 15) Is C ⊂ D given C = {1,2,3,4,5}, D = {1,2,3,4} Answer: no, C is not contained in D, so this is not true 17) Is A ⊂ B given A = {4,3,2,1 }, B = {1,2,3,4,5} A is a set so rule 1 is satisfied, A is contained in B so rule 2 is satisfied A is not equal to B so rule 3 is satisfied Answer: yes (all 3 rules are satisfied) Homework #19 – 34: Determine which of these are true. (Choose every answer that is true, in many instances there will be more than one correct choice.) A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A, or none of these 19) A = {Trix, Captain Crunch, Rice Krispees} B = {Rice Krispees} B is contained, but not equal to A. B is both a subset and a proper subset of A. A is not contained in B The sets are not equal. Answer: B ⊆ A, B ⊂ A 21) A = {5,7,9} B = {9, 5, 7} The two sets are equal. All notation with an equal sign will be true. The notation without the equal sign A ⊂ B, B ⊂ A are not true when the sets are equal. Answer: A = B, A ⊆ B, B⊆A 23) A = {2,4,6} B = {2,4,6,8} A is contained and not equal to B. both A ⊆ B, A ⊂ B are true B is not contained in A so neither B ⊂ A, B⊆A are true Answer: A ⊆ B, A ⊂ B 25) A = {a,b,c} B = {a,b,d} These are equivalent, but that isn’t asked in this question. A is not contained in B as there is a “c” in A that is not in B. B is not contained in A as there is a “d” in B that is not in A. Answer: none 27) A = {푥|푥 ∈ 푁 푎푛푑 푥 < 9} B = {4,5,6} A = {1,2,3,4,5,6,7,8} A is certainly not contained in B. B is contained but not equal to A so these are both true: B ⊆ A, B ⊂ A Answer: B ⊆ A, B ⊂ A 29) A = {8,9,10,11…} B = {푥|푥 ∈ 푁 푎푛푑 푥 ≥ 9} B = {9,10,11,12…} A is contained in B and A is not equal to B so these are true: A ⊆ B, A ⊂ B B is not contained in A so neither of these are true: B ⊆ A, B ⊂ A Answer: A ⊆ B, A ⊂ B 31) A = {푥|푥 ∈ 푁 푎푛푑 2 < 푥 < 9} B = {3,4,5,6,7,8} A = {3,4,5,6,7,8} The sets are equals. Only the symbols with the equal signs are true. Answer: A = B, A ⊆ B, B ⊆ A, 33) A = {푥|푥 ∈ 푁 푎푛푑 2 < 푥 < 9} B = {0,1,2,3,4,5,6,7,8} A = {3,4,5,6,7,8} A is contained but not equal to B, so these are true: A ⊆ B, A ⊂ B B is not contained in A so these are not true: B ⊆ A, B ⊂ A Answer: A ⊆ B, A ⊂ B .