Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is an equilateral triangle in a plane $\} \ldots \{ x:x$ is a triangle in the same plane $\} $
$\{ x:x$ is an equilateral triangle in a plane $\} \subset \{ x:x$ is a triangle in the same plane $\} $
Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$
Write the following intervals in set-builder form :
$\left[ {6,12} \right]$
Which of the following are sets ? Justify your answer.
The collection of ten most talented writers of India.
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 $x \in A$ and $A \in B,$ then $x \in B$
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$10 \, .........\, A $