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