Tamil Nadu Board Solutions for Chapter: Set Language, Exercise 13: Exercise

If $P=\{1,2,5,7,9\}, Q=\{2,3,5,9,11\}$ and $R=\{3,4,5,7,9\}$, then find $(P\cup Q)\cup R$.

If $P=\{1,2,5,7,9\},Q=\{2,3,5,9,11\}$ and $S=\{2,3,4,5,8\}$, then find $(P\cap Q)\cap S$.

If $Q=\{2,3,5,9,11\}, R=\{3,4,5,7,9\}$ and $S=\{2,3,4,5,8\}$, then find $(Q\cap S)\cap R$.

Test for the commutative property of union and intersection of the sets $P=\{x:x$ is a real number between $2$ and $7$}  and 
$Q=\{x:x$ is an irrational number between $2$ and $7$}.

(Consider a proper single integer value for the rational number or irrational number; Note: Don't take any decimal values)

If $A=\{p,q,r;s\},B=\{m,n,q,s,t\}$ and $C=\{m,n,p,q,s\}$ , then verify the associative property of union of sets

Verify the associative property of intersection of sets for $A=\{-11,\sqrt{2},\sqrt{5},7\}$$B=\{\sqrt{3},\sqrt{5},6,13\}$ and $C=\{\sqrt{2},\sqrt{3},\sqrt{5},9\}$.

If $A=\left\{x:x=2^n, n\in W\right.$ and $n<4\}, B=\{x:x=2n, n\in \mathrm{\mathbb{N}}$ and $n\le 4\}$ and $C=\{0,1,2,5,6\}$, then verify the associative property of intersection of sets.

Are $P=\left\{x:-3\le x\le 0, x\in \mathrm{\mathbb{Z}}\right\}$ and $Q=$ The set of all prime factors of $210$, equivalent sets?