Chapter 1: Sets

Exercise

Question

Question: 3 (v)

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State whether each of the following set is finite or infinite:

(v) The set of circles passing through the origin (0, 0)

Answer

1
Determine whether there is a fixed number of circles passing through the origin (0, 0).
Answer: It is an infinite set.
Reason: Infinitely many circles can pass through a fixed point by varying their centers and radii. Therefore, the set has infinitely many elements and is an infinite set.
Examples: Circle with centre (1,0) and radius 1, Circle with centre (2,0) and radius 2, Circle with centre (3,0) and radius 3, and so on indefinitely.
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