Which of the following sets are finite and which are infinite? (i) Set of concentric circles in a plane. (ii) Set of letters of the English Alphabets. (iii) (x ∈N : x greater than 5} (iv) {x ∈N : x less than 200} (v) {x ∈Z : x less than 5} (vi) {x ∈R : 0 less than x less than 1}.

Finite and Infinite Sets

Set	Finite / Infinite	Reason
(i) Set of concentric circles in a plane	Infinite Set	Infinitely many concentric circles can be drawn.
(ii) Set of letters of the English alphabets	Finite Set	There are only \[ 26 \] letters.
(iii) \[ \{x\in N:x>5\} \]	Infinite Set	Natural numbers greater than \[ 5 \] continue endlessly.
(iv) \[ \{x\in N:x<200\} \]	Finite Set	Only finitely many natural numbers are less than \[ 200 \]
(v) \[ \{x\in Z:x<5\} \]	Infinite Set	Integers less than \[ 5 \] extend indefinitely in the negative direction.
(vi) \[ \{x\in R:0	Infinite Set	Infinitely many real numbers lie between \[ 0 \] and \[ 1 \]

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Finite and Infinite Sets