Question

State whether the following sets are finite or infinite
(i) $A=$ { $x:x$ is a multiple of 5, $x\in N$ }
(ii) $B=$ { $x:x$ is an even prime number }
(iii) The set of all positive integers greater than 50.

Answer 1

(i) $A=$ { $x:x$ is a multiple of 5, $x\in N$ } $=\{5,10,15,20,...\}$
$\therefore A$ is an infinite set.
(ii) $B=$ { $x:x$ is an even prime numbers }. The only even prime number is 2.
$\therefore B=\left\{2\right\}$ and hence $B$ is a finite set.
(iii) Let $X$ be the set of all positive integers greater than 50. Then $X=\{51,52,53,...\}$
$\therefore X$ is an infinite set.