True or False: $A_i$ Set Theory

Question

$\displaystyle \bigcap_{i=1}^nA_i\subseteq \bigcap_{i=1}^{m+n}A_i\ $ and $m>0$

I have to describe whether or not this statement is true. From my understanding it is False, but I'm not sure if my logic is flawed.

I took an example where $m=1$ and $n=1$

$\displaystyle \bigcap_{i=1}^1A_i\subseteq \bigcap_{i=1}^{1+1}A_i\ $

$A_1 \subseteq (A_1 \cap A_2)$

So as $m$ increases the intersection would have a smaller probability of being a superset of $\displaystyle \bigcap_{i=1}^nA_i$

Don't think about probability (although your intuition is correct). Try to give a concrete example in which the claim fails. — Bach, Feb 10 '14 at 18:23

score 0 · Accepted Answer · answered Feb 10 '14 at 18:23

0

You are exactly right. Anyway, you should give an example of $A_1$ and $A_2$. You could take $A_1=\{\emptyset\}$, $A_2=\emptyset$.

answered Feb 10 '14 at 18:23

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