Consider a general set, A, which is a subset of a general set, Ω. Suppose also that B is the complement of A, i.e. B=Ac=Ω∖A.Next let C be a subset of A (i.e. C⊆A) and D be a subset of B (i.e. D⊆B).Tick the most appropriate answer:B⊆DA∖C=C(C∪D)c=Cc∩DcAll of the above
Question
Consider a general set, A, which is a subset of a general set, Ω. Suppose also that B is the complement of A, i.e. B=Ac=Ω∖A.Next let C be a subset of A (i.e. C⊆A) and D be a subset of B (i.e. D⊆B).Tick the most appropriate answer:B⊆DA∖C=C(C∪D)c=Cc∩DcAll of the above
Solution
The correct answer is (C∪D)c=Cc∩Dc.
Here's why:
-
B⊆D: This is not necessarily true. B is the complement of A, and D is a subset of B. It's possible that D is a smaller set than B, so B is not necessarily a subset of D.
-
A∖C=C: This is not true. A∖C means the set of elements in A that are not in C. Since C is a subset of A, A∖C would be the elements of A that are not in C, which is not the same as C.
-
(C∪D)c=Cc∩Dc: This is true according to De Morgan's laws. The complement of the union of two sets is equal to the intersection of their complements.
So, the most appropriate answer is (C∪D)c=Cc∩Dc.
Similar Questions
De Morgan's Law allows us to express the complement of the union of two sets in terms of:a.The union of the complements of the setsb.The intersection of the complements of the setsc.The complement of the intersection of the setsd.The complement of the symmetric difference of the sets
Let C and D be two sets then C – D is equivalent to __________a.C’ ∩ Db.None of the mentionedc.C‘∩ D’d.C ∩ D’
If A ⊂ B and B ⊂ C, what can we conclude?a.A = Cb.C ⊂ Ac.B = Cd.A ⊂ C
Define: Set, Subset, Complement
Let 𝐴 and 𝐵 be sets. Show thata) (𝐴 ∩ 𝐵) ⊆ 𝐴.b) 𝐴 ⊆ (𝐴 ∪ 𝐵).c) 𝐴 − 𝐵 ⊆ 𝐴.d) 𝐴 ∩ (𝐵 − 𝐴) = ∅.e) 𝐴 ∪ (𝐵 − 𝐴) = 𝐴 ∪ 𝐵.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.