Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to
$25$
$34$
$42$
$41$
Total number of unordered pairs of disjoint subsets
$=\frac{3^4+1}{2}=41 \text {. }$
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \subset B$ and $B \in C,$ then $A \in C$
If $x \in A$ and $A \not\subset B$, then $x \in B$
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is a triangle in a plane $\} \ldots \{ x:x$ is a rectangle in the plane $\} $
Given the sets $A=\{1,3,5\}, B=\{2,4,6\}$ and $C=\{0,2,4,6,8\},$ which of the following may be considered as universal set $(s)$ for all the three sets $A$, $B$ and $C$
$\{ 0,1,2,3,4,5,6\} $
State which of the following sets are finite or infinite :
$\{ x:x \in N$ and $(x – 1)(x – 2) = 0\} $
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