Let T and M be a non-empty families of sets with T  ⊆ M. Show that ∩T  ⊆ ∪ M.

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: Let T be the set of all TSU students. Determine if (T, R) a poset or not if R = {(a, b)|a ∈ T, b ∈…

A: 1 We  List all of the ordered pairs in the relation R = {(a, b)|a + b is even} on the set {1, 2, 3,…

Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅. Let the universal set U be {1,…

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Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

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Q: Let A, B, and C be subsets of a universal set U and suppose n(U)= 150, n(A) = 22, n(B) = 24, n(C) =…

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Q: Let A and B be sets. Suppose that A ⊆ B. Prove that P(A) ⊆ P(B)

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Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

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Q: Prove that for all sets A and B, A – B = AN B

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Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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Q: Let A and B be subsets of some universal set U. Prove each of the following: *(a) An BCA * (b) A…

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Q: Let A and B be two sets. a) Suppose that A and B are both countably infinite sets. Prove that there…

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Q: Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A…

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Q: Let U be the universal set with disjoint subsets A and​ B, where n(U) = 37​, n(A) = 8​, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law  A'∩B' =…

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Prove that if X ∩ Y = X ∩ Z and X ∪ Y = X ∪ Z, then Y = Z for all sets X, Y , and Z.

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Q: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

Q: Suppose F and G are families of sets. Prove that (UF)n (UG) ≤ U(F N G) iff VA EFVBE G(An BCU (FNG)).

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Q: Let A, B1, B2 and C be sets and let B AC BỊ and C C B2. Bị × B2. Consider the statement, "If A x C C…

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