Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have to say if {2} is an element of the given sets. I'm reading {2} as if it was a subset which would make the problem true for C, D and E only correct?

F it isn't because that is a nested subset and A/B don't contain subsets.

For each of the sets, determine whether {2} is an element of that set.
a) {x ∈ R | x is an integer greater than 1}
b) {x ∈ R | x is the square of an integer}
c) {2,{2}}
d) {{2},{{2}}}
e) {{2},{2,{2}}}
f ) {{{2}}}

share|improve this question
6  
Looks like you're on the right track. –  Andrew Jul 10 '12 at 20:34

1 Answer 1

up vote 3 down vote accepted

First recall that $a$ is an element of $b$ if and only if $a\in b$. On the other hand, $a$ is a subset of $b$ if and only if for every $x$ such that $x\in a$, $x\in b$.

My usual tip in this situation is to replace $\{2\}$ by $x$. Now we can think of the given sets,a,b are both sets of numbers, now we can see that $x$ is not an integer, nor a real number, so it is not in either a or b.

On the other hand, c can be written as $\{2,x\}$, which means that $x$ is an element of this set. Similarly d,e both have $x$ as an element. However what is the set f? $\{\{\{2\}\}\}=\{\{x\}\}$ and $x$ is not an element of this set, it is rather an element of an element of this set.

share|improve this answer
    
Is your first sentence really what you intended to write? It is a tautology that gives no information unless the reader does not know the meaning of the symbol $\in$. –  Rahul Jul 10 '12 at 21:55
    
@RahulNarain: There is always confusion; e.g., does "X contains 2" mean $2\in X$, or does it mean $2\subseteq X$? (Recall that $2$ is itself a subset). Perhaps Asaf is thinking along those lines, and something got lost in the translation... –  Arturo Magidin Jul 10 '12 at 23:52
    
@Rahul: The $\in$ relation is atomic, how would you express it? It seems a bit strange to write this first sentence, but this is the same as truth definition "$\varphi\land\psi$ is true if and only if $\varphi$ and $\psi$ are true". –  Asaf Karagila Jul 11 '12 at 5:52

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.