15 items are filed under this topic.








nC0 + nC1 + nC2 + .... + nCn = 2^n 
20180219 

From bristal: (QQ) Prove, nC0 + nC1 + nC2 + .... + nCn = 2^n. Answered by Penny Nom. 





Subsets 
20160626 

From Kats: How Many sub sets are in set k={6,7,3} Answered by Penny Nom. 





The number of possible musical notes using an nkey instrument 
20150504 

From Farihin: Lets say that i have keys, and each key is for notes of a musical instrument,
So i wanted to find out the number of notes i can get for a certain number keys,
of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100.
Notes in real life is not as such, but ignore reality.
I tried doing this but i can't seem to find a formula for it.
For example, i have 4 keys, say A, B, C, and D.
so, for notes that uses one key are 4, which is A, B, C, and D themselves.
for notes that uses two keys are 6,
AB, AC, AD, BC, BD and CD.
for notes that uses three keys are 4,
ABC, ABD, ACD and BCD.
lastly for notes that uses all four keys is 1, ABCD.
So, the total will be 4+6+4+1=15#
The nth term for the first equation is n, the second is [(n^2)n]/2
the third and the fourth, i don't know but the final answer should be like,
n + [(n^2)n]/2 + [3rd] + [4th]
Sorry for the long question though... Answered by Penny Nom. 





A question in set theory 
20150225 

From Jared: If a set A={1,2,3} and set B={ {}, 1}
Can B be a subset of A? Since every Set contains an {} ? Answered by Robert Dawson and Claude Tardif. 





Properties of real numbers applied to subsets 
20120201 

From Mark: Hello 
The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Answered by Robert Dawson. 





Subsets 
20090616 

From Tracy: Suppose C is the subset of D and D is the subset of C.
If n(c)=5, find n(D)
What other relationship exists between sets C and D? Answered by Penny Nom. 





Subsets of a set 
20071030 

From Snehal: 1. Let an denote the number of subsets of f{1,2, 3.... n}including the
empty set and the set itself.)
a) Show an = 2an1
b) Guess a formula for the value of an and use induction to prove you are
right Answered by Stephen La Rocque. 





Equality of sets 
20070723 

From Mac: Hi, I learnt set theory recently. My teacher and few of the weblink actually give different
definition for basic set. Can you please solve this ?
My teacher says, {1,2,3} and {1,1,2,3} is also set.
But in this link http://library.thinkquest.org/C0126820/setsubset.html it says,
"A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice."
and "{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}"
My question is,
1. Whether duplicates allowed in the set or not ?
2. Even if the duplicates are allowed, {1,2,3} and {1,1,2,2,3,3} are same or not ? Answered by Penny Nom and Harley Weston. 





The empty set is a subset of every set 
20061114 

From Narayana: The empty set is a subset of every set Answered by Stephen La Rocque and Penny Nom. 





Onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5 
20061009 

From Hina: If onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m. Answered by Steve La Rocque and Claude Tardif. 





B={A,{A}} 
20040920 

From Muhammad: Let A be a set and let B = {A,{A}}.
(a) Explain the elements of set B (with some example)
(b) Prove that A is not a subset of B. Answered by Penny. 





Combinations of 1,2,3,...,10 
20021127 

From Gord: If I had the numbers from 110 how many different combinations would i have.....would it be 100....since that is 10 squared. Answered by Penny Nom. 





Sets and elements 
20020822 

From Dianne: I want to know why its okay to say that, for example, 6 is an element of the set of integers, but you get counted off for saying that the set of 6 is an element of the set of integers. How come? Answered by Judi McDonald. 





Subsets of a countably infinite set 
20011114 

From Tania: How could I show (and explain to my son) that any countably infinite set has uncontably many infinite subsets of which any two have only a finite number of elements in common? Answered by Claude Tardif. 





Subsets of the natural numbers 
20010130 

From Christina: How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Answered by Penny Nom. 


