Set Theory

A total of 83 teens attended performing arts camp to train in at least one of three activities: dance, acting, or singing. 50 took dana ce, 50 took acting, and 44 took singing 15 took dance and acting...

Suppose we partition the reals into two sets $A$ and $B$ that are dense (with positive Lebesgue measure) in every non-empty sub-interval $(a,b)$ of $\mathbb{R}$, where Lebesgue measure $\lambda$ restr...

Suppose we partition the reals into two sets $A$ and $B$ that are dense and has positive Lebesgue measure in every non-empty sub-interval $(a,b)$ of $\mathbb{R}$, where Lebesgue measure $\lambda$ rest...

Please help me with the question attached below.

I need help with the question below. I would really appreciate if you can solve it for me. 

Need Help with the discrete math question in the image below. You need to use the Deza-Frankl-Singhi theorem to solve it. 

Hey guys, Maybe someone of you can help. I need to prove the following through inclusion: (A∆B) ∪ A = A ∪ BAny suggestion on how to solve this?

I'm reading J. Neveu's "Mathematical Foundations of the Calculus of Probability". There is a question regarding the Souslin operation and proving it is idempotent. In essence, we start with a collecti...

I am reading J. Neveu's "Mathematical foundations of the calculus of probability." There he presents what he calls a distributivity formula: \bigcup_{j \in J} \bigcap_{i \in I_j} F_i^j=\bigcap_{\{i_j\...

Let $FS(α, β) ⇋ { f | f : β->α & Fin( {γ | γ ∈ β & not( f(γ) = 0 ) })}$ for all ordinals α, β,where Fin(A) means the set A is finite. We define a relation ≺ on FS:  $f ≺ g ←→ (∃γ < β)( f...

Hi, I need to answer this question:Find a system consisting of two sets, neither of which is a subset of the other.I will be very grateful if someone helps me!

We have $k,m \in \N^*$. Define two sets U and V by:U = {$a \in \Z | 1 \leq a \leq m, gcd(a,m) = 1$}V = {$a \in \Z | 1 \leq a \leq km, gcd(a,km) = k$}a. We have $a \in U$. Show that $ka \in V$b. Thanks...

Here’s my question:I have a set that looks like this: S = {u, v , w , x , y , z} And it has this restriction:1 =< u < v < w < x < y < z <= 11 Essentially, of 6 values, all of them...

We have $b_n$ a sequence defined by:$b_n = $ (1 if n is primary, 0 if not) Let there be a $x \in \R$ such that its decimal representation is $x = 0, b_1 b_2 b_3 ....$a. Prove that $x \notin \mathbb{Q}...

 Question I want to find a measure of uniformity that determines the most "uniform" "structure" for the most cases of countably infinite sets?  Definition of Structure A "structure" of a countably inf...

Problem 1: Suppose we wish to construct a password of length 20, which may include the following characters: 9 special characters, 10 numbers, 26 lowercase letters, and 26 uppercase letters. The passw...

The problems is exactly what is stated in the title. Have been stuck on this for a while now. Thanks. 

Need a Solution to the following questionLet $\Sigma$ be the alphabet defined as follows: $\Sigma = {e, l, v}$. We now deifine the set of strings P according to the following:BASIS STEP: If $x \in \Si...