Which of the following sets are finite and which are infinite?

Question:

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 > 5};

(iv) {x = ∈ N : x < 200};

(v) {x ∈ Z : x < 5};

(vi) {x ∈ R : 0 < x < 1}.

Solution:

(i) There can be infinite concentric circles in a plane. Therefore, it is an infinite set.

(ii) There are 26 letters in the set of English alphabet. Therefore, it is a finite set.

(iii) {x ∈ N : x > 5} = {6,7,8,9,...}. There will be infinite numbers. So, it an infinite set.

(iv) There are finite elements in the set {x = ∈ N : x < 200}. Therefore, it is a finite set.

(v) In this set, x ∈ Z , so there would be infinite elements in the set {x ∈ Z : x < 5}. Therefore, it is an infinite set.

(vi) In this set,  x ∈ R. We know real numbers include all numbers, i.e., decimal numbers, rational numbers and irrational numbers.

So, there would be infinite elements in the set {x ∈ R : 0 < x < 1}. Therefore, it is an infinite s

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