What universal set $(s)$ would you propose for each of the following :

The set of right triangles

Which of the following sets are finite or infinite.

$\{1,2,3, \ldots 99,100\}$

Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{1,2,5\}\subset A$

Which of the following are sets ? Justify your answer.

A team of eleven best-cricket batsmen of the world.

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 $B = C$