What is the difference between contained and strictly contained. I know contained has to do with subsets and strictly contained involves proper subsets but Im not sure what that really means. My guess is that is element B was scattered within A then its a subset, but if element be was in a really small bubble and could ONLY be in that area within A then its a proper subset.
weisbart: Jan. 14, 2015, 8:49 a.m.
To say that $A$ is a subset of $B$ (or $A$ is contained in $B$) means that everything in $A$ is also in $B$. However, $A$ and $B$ might actually be equal. In this case, $A$ is still a subset of $B$. We use the word strict containment and say that $A$ is strictly contained in $B$ or a proper subset of $B$ if $A$ is contained in $B$ but $B$ is not equal to $A$, it is actually larger than $A$. This means that everything in $A$ is also in $B$, but there is something in $B$ that is not in $A$. \[\] Look at the following example. Suppose that \[A = \{a,b,c\} \quad {\rm and}\quad B = \{a,b,c,d\}.\] Here, $A$ is strictly contained in $B$ ($A\subset B$) because everything in $A$ is in $B$ but $B$ contains an element, $d$, that is not in $A$. \[\] Does this make sense? Don't get too bogged down with language, the most important thing is to work lots of counting problems.