Question
Which of the following sets is a finite set ?
A.
$$A = \left\{ {x:x\, \in \,Z{\text{ and }}{x^2} - 5x + 6 = 0} \right\}$$
B.
$$B = \left\{ {x:x\, \in \,Z{\text{ and }}{x^2}{\text{ is even}}} \right\}$$
C.
$$D = \left\{ {x:x\, \in \,Z{\text{ and }}x > - 10} \right\}$$
D.
All of these
Answer :
$$A = \left\{ {x:x\, \in \,Z{\text{ and }}{x^2} - 5x + 6 = 0} \right\}$$
Solution :
$$\eqalign{
& \left( {\text{A}} \right)\,\,A = \left\{ {x:x\, \in \,Z{\text{ and }}{x^2} - 5x + 6 = 0} \right\} = \left\{ {2,\,3} \right\} \cr
& {\text{So, }}A{\text{ is a finite set}}{\text{.}} \cr
& \left( {\text{B}} \right)\,\,B = \left\{ {x:x\, \in \,Z{\text{ and }}{x^2}{\text{ is even}}} \right\} \cr
& = \left\{ {.....,\, - 6,\, - 4,\, - 2,\,0,\,2,\,4,\,6,.....} \right\} \cr
& {\text{Clearly, }}B\,{\text{is an infinite set}}{\text{.}} \cr
& \left( {\text{C}} \right)\,\,D = \left\{ {x:x\, \in \,Z{\text{ and }}x > - 10} \right\} \cr
& = \left\{ { - 9,\, - 8,\, - 7,.....} \right\} \cr
& {\text{Clearly, }}D\,{\text{is an infinite set}}{\text{.}} \cr} $$