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 a bit difficulty :

If A,B and C are sets then:

  • A ∈ B , B ⊆ C.Then A ⊆ C is true.
  • A ⊄ B.Then B ⊂ C is true.
  • C ∈ p(A) iff C ⊆ A, where p(A) denotes the power of set A.

All are correct?It's confusing me alot.

Basically i am a CS student, very poor in maths, but now have to do it, as maths is applicable everywhere.

Also please suggest me few tips and logics to study maths in a easy way.

Thank You

share|improve this question
add comment

1 Answer

up vote 3 down vote accepted

Your first point would be correct if you either changed "$A\subseteq C$" to "$A\in C$", or changed "$A\in B$" to "$A\subseteq B$". The first change works because $B\subseteq C$ means every element of $B$ is an element of $C$, so if $A\in B$, then $A$ in $C$. The second change works because $A\subseteq B$ means every element of $A$ would be an element of $B$, so since every element of $B$ is an element of $C$, then every element of $A$ is an element of $C$, meaning $A\subseteq C$.

Your second point is incorrect. Knowing only that $A\not\subset B$ (that is, that some element of $A$ isn't in $B$) tells us nothing about whether all the elements of $B$ are all in $C$.

Your third point is correct. The $\mathcal{P}(A)$ is defined to be the set of all $C$ such that $C\subseteq A$. Thus, $C\subseteq A$ if and only if $C\in\mathcal{P}(A)$.

share|improve this answer
    
So, what is given, the 1st point is incorrect? –  joey rohan Mar 25 '13 at 12:22
    
As stated, it is incorrect. Given $A\in B$ and $B\subseteq C$, we can only conclude that $A\in C$ (by definition of the statement "$B\subseteq C$"), and not necessarily that $A\subseteq C$. –  Cameron Buie Mar 25 '13 at 12:24
    
@joeyrohan My mistake. The first point is INCORRECT, I just read it wrong. You have my apologies. –  user18921 Mar 25 '13 at 12:26
    
Thank you :) Can you please just give me 2 more suggestions?1) how to use symbols like ⊆ , P or something, is there a simple way? 2) The latter part,how to study maths in a logical way? any help would be much appreciated.Thank you! –  joey rohan Mar 25 '13 at 12:31
    
@joeyrohan I'd love to be able to tell you how to study maths in a logical way, but unfortunately I have yet to find one! Maybe check amazon for a highly rated introduction to logic? I presume there are works written for philosophy students, which should probably be accessible. Or buy a book about how to prove things. Again, search amazon. –  user18921 Mar 25 '13 at 12:40
show 1 more comment

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.