Are Small (or Even Mid) Cap Fund Returns Limited Because of Market Cap Rules?

In theory you might be correct. In practice I suspect that would seldom happen. You need to understand that Google was never a small cap. It started out as a large cap the day it went public. Same with MSFT. The other thing to take into account is that the largest holding of VSISX makes up only 0.25% of the portfolio, so even if one of those holdings does go gang busters it is not going to make a big difference in the overall performance of the fund

1. Should there be a salary cap in football?

No. "Fair" is not part of the equation. Football is a business, just like any other. It's the biggest sport in the world. There are enough regulations on the field - why add more off of it?

2. A sufficient and necessary condition for $Acup (B cap C) = (A cup B) cap C$

Claim: If $Asubset C$ then $Acup(Bcap C)=(Acup B)cap C$.Proof: This is "obvious", since $Acup(Bcap C)=(Acap C)cup(Bcap C)=(Acup B)cap C$.Claim: If $Acup(Bcap C)=(Acup B)cap C$ then $Asubset C$.Proof: Suppose that $A

otsubset C$. Then the Left Hand Side (LHS) of our equality is also not a subset of $C$, but the Right Hand Side (RHS) is, a contradiction.

3. Is this a valid proof of $f(S cap T) subseteq f(S) cap f(T)$?

What if there's an element that is in the $S cap T$ that also maps to $y$? In other words, what if $f$ is not injective? I honestly stopped reading there. Usually when showing that a set is a subset of another, you want to take a direct approach. I am not saying that a contradiction would not work, and I believe that in more complicated situations it would, but for simple properties like this, you should try a direct approach first:I will be informal (or at least not use symbols), so you can seen if you understand the proof and write it yourself. You pick an element in the set on the left, and you see that its preimage sits in $Scap T$. This just follows from the definition of the preimage. So the preimage sits in both $S$ and $T$. Now apply $f$ to the elements in the preimage, what do you get?

4. Smoke comming from Oil Cap?

That condition is referred to as blow-by, and it is a result of piston rings not sealing properly anymore due to wear. You should try dumping a bottle of slick-50 into the engine to see if that helps any, otherwise, the engine would need to be overhauled

5. Prove that $Acap B= emptyset$ iff $A cap B' = A$

we can easily interpret this in a Venn diagram for understanding

6. WHAT IS STEEL TOE CAP?

It is shoes that have steel at the toes to prevent them from being crushed

7. Which are the best mutual funds in large-cap, mid-cap, small-cap, balance, and diversified equity funds?

Based on our research, we recommend the following portfolio of MF. The investment amount can be bifurcated based on individuals risk profiling and goal duration

8. How is this kind of cap called?

umm... winter hat?

9. The ‘Cap And Tax' Dead End..?

The other countries are laughing at America. They understand Obama will tax American business right into their hands and countries. They are laughing

10. Prove $Acap A = A$.

Proof using only set algebra laws ( without analyzing the propositions in termes of set theoretic membership). $A$$= A cap U $$= A cap ( A cup A^c)$$= (A cap A) cup (A cap A^c)$$= (A cap A) cup $ $= A cap A$Laws Used $X cap U = X$ ( and reciprocally) $X cup X^c = U$ ( and reciprocally) $X cap ( Y cup Z) = (X cap Y) cup ( X cap Z)$$X cap X' = $ $X cup = X$

11. How would you describe a maids uniform?

black dress with white apron and cap. white nurse type shoes

12. I forgot to put the Oil cap on?

Leaving the oil cap off usually just makes a mess. Did you check the oil after putting the cap back on? Is your coolant still topped up? I am guessing you have a coincidence on your hand and have another problem.