Question

Find, which of the following sets are empty:

(i)The set of points of intersection of two parallel lines.

(ii) $A=\{x:x\in Nand5<x\le 6\}$

(iii) $B=\{x:x^2+4=0,x\in N\}$

(iv)$C=\left\{evennumbersbetween6\&10\right\}$

(v) $D=\left\{primenumbersbetween7\&11\right\}$

Note : The set, which has no element in it, is called the empty or null set.

Answer 1

(i)"The set of points of intersection of two parallel lines" is an empty set because two parallel lines do not intersect anywhere. Ans.

(ii)$A=\{x:x\in Nand5<x\le 6\}As5<x\le 6\therefore x=6\therefore A=\left\{6\right\}\text{Hence given set A is not an empty set. Ans.}\left(iii\right)\{x:x^2+4=0,x\in N\}{x}^2+4=0\Rightarrow x^2+4=0\Rightarrow x^2=-4\Rightarrow x=\sqrt{-4}\text{which is not a natural number.}\left\{evennumbersbetween6\&10\right\}Butx\in N\therefore B=\left\{\right\}\therefore \text{Given set B is an empty set. Ans.}$

(iv) $C=\left\{Evennumbersbetween6and10\right\}\therefore C=\left\{8\right\}\text{Hence it is an empty set. Ans.}$

(v) $D=\left\{primenumbersbetween7\&11\right\}\text{Because there is no prime number between 7~and~11.}\therefore D=\left\{\right\}$