Question

Let S be a collection of subsets of [n] such that any two subsets in S...

Let S be a collection of subsets of [n] such that any two subsets in S have a non-empty intersection. Show that |S| ≤ 2^(n−1).

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Proof attached

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let S be the sample space of an experiment and let ℱ be a non-empty collection...
Let S be the sample space of an experiment and let ℱ be a non-empty collection of subsets of S such that i) ? ∈ ℱ ⇒ ? ′ ∈ ℱ and ii) ?1 ∈ ℱ and ?2 ∈ ℱ ⇒ ?1 ∪ ?2 ∈ ℱ a) Show that if ?1 ∈ ℱ and ?2 ∈ ℱ then ?1 ∩ ?2 ∈ ℱ . b) Show that ? ∈ ℱ. c) Is ℱ necessarily a ?-algebra? Explain briefly. A rigorous...
Let f : X → Y and suppose that {Ai}i∈I is an indexed collection of subsets...
Let f : X → Y and suppose that {Ai}i∈I is an indexed collection of subsets of X. Show that f[∩i∈IAi ] ⊆ ∩i∈I f[Ai ]. Give an example, using two sets A1 and A2, to show that it’s possible for the LHS to be empty while the RHS is non-empty.
Let X be a set and let (An)n∈N be a sequence of subsets of X. Show...
Let X be a set and let (An)n∈N be a sequence of subsets of X. Show that: (a) If (An)n∈N is increasing, then liminf An = limsupAn =S∞ n=1 An. (b) If (An)n∈N is decreasing, then liminf An = limsupAn =T∞ n=1 An.
Let {??}?∈? be an indexed collection of subsets of a set ?. Prove: a. ?\(⋃ ??)...
Let {??}?∈? be an indexed collection of subsets of a set ?. Prove: a. ?\(⋃ ??) ?∈? = ⋂ (?\??) ?∈? b. ?\(⋂ ??) = ⋃ (?\??) ?∈?? ∈? Note: These are DeMorgan’s Laws for indexed collections of sets.
Let n ≥ 2 be any natural number and consider n lines in the xy plane....
Let n ≥ 2 be any natural number and consider n lines in the xy plane. A point in the xy plane is called an intersection point if at least two lines pass through it. Use induction to show that the number of intersection points is at most (n(n-1))/2.
Let A, B be non-empty subsets of R. Define A + B = {a + b...
Let A, B be non-empty subsets of R. Define A + B = {a + b | a ∈ A and b ∈ B}. (a) If A = (−1, 2] and B = [1, 4], what is A + B?
Suppose that the set S has n elements and discuss the number of subsets of various...
Suppose that the set S has n elements and discuss the number of subsets of various sizes. (a) How many subsets of size 0 does S have? (b) How many subsets of size 1 does S have? (c) How many subsets of size 2 does S have? (d) How many subsets of size n does S have? (e) Clearly the total number of subsets of S must equal the sum of the number of subsets of size 0, of size...
Let S be a finite set and let P(S) denote the set of all subsets of...
Let S be a finite set and let P(S) denote the set of all subsets of S. Define a relation on P(S) by declaring that two subsets A and B are related if A and B have the same number of elements. (a) Prove that this is an equivalence relation. b) Determine the equivalence classes. c) Determine the number of elements in each equivalence class.
1)Let the Universal Set, S, have 97 elements. A and B are subsets of S. Set...
1)Let the Universal Set, S, have 97 elements. A and B are subsets of S. Set A contains 45 elements and Set B contains 18 elements. If Sets A and B have 1 elements in common, how many elements are in A but not in B? 2)Let the Universal Set, S, have 178 elements. A and B are subsets of S. Set A contains 72 elements and Set B contains 95 elements. If Sets A and B have 39 elements...
Let S and T be nonempty subsets of R with the following property: s ≤ t...
Let S and T be nonempty subsets of R with the following property: s ≤ t for all s ∈ S and t ∈ T. (a) Show that S is bounded above and T is bounded below. (b) Prove supS ≤ inf T . (c) Given an example of such sets S and T where S ∩ T is nonempty. (d) Give an example of sets S and T where supS = infT and S ∩T is the empty set....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT