wicked scarab
is it true that $ C \subseteq (A \cap B) \implies C \subseteq A$ and $C \subseteq B$?
I know that $c \in A \cap B \implies c \in A$ and $c \in B$ by definition of set intersection, I was just wondering if there was an analogous proposition for subsets of intersections
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sage spear
\left|C \right|\leq \left|A \cap B \right|\leq \left|A \right|
This proves size for strict subset and since C is a subest of A intersect B, C is a subset of both A and subset fof B, therefore making it a strict subest of both
wait it doesnt state that A and B are not the same set
If A and B are not the same set then it holds true
wicked scarab
$\left|C \right|\leq \left|A \cap B \right|\leq \left|A \right|$
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