Question

State whether the following set is finite or infinite?
Set of concentric circles in a plane.

Answer 1

Hint: Finite means we can count the elements, infinite means which we can’t count how many elements are present.

Complete step-by-step answer:

Concentric Circles: These are the circles having the same centre but having different radius shown in the as shown in the diagram.
Here circle ${\text{g, c, d, e, f, h}}$ having the same centre ${\text{A}}$. We can draw infinitely many circles through centre ${\text{A}}$.
Therefore, in a given plane there are infinitely many concentric circles such that the set of concentric circles is infinite.
Therefore, Given Set is an infinite set.

Additional Information: A set is a well defined collection of distinct objects. The objects that make a set are also called elements.
Example -
Collection of all months of year is a set because months of a year can be counted therefore it is a finite set.
Collection of ten most talented persons in India is not a set because talent varies from person to person therefore it is not well defined; therefore it is not a set.
The collection of questions in this Chapter is a set because question can be counted in a chapter therefore it is well defined set
Collection of all even numbers belongs to Natural Numbers is a set because it can be counted however it is infinite numbers, therefore it is infinite set.

Note: While answering the statement question of set first always check the given statement is actually a set i.e., well defined set or not.