State which of the following sets are finite or infinite. (i) {x : x

1.	State which of the following sets are finite or infinite. (i) {x : x ∈ N and (x – 1)(x – 2) = 0} (ii) {x : x ∈ N and x2 = 4} (iii) {x : x ∈ N and 2x-1 = 0} (iv) {x : x ∈ N and x is prime} (v) {x : x ∈ N and x is odd} (vi) The set of lines which are parallel to the x-axis. (vii) The set of letters in the English alphabet. (viii) The set of numbers which are multiple of 5. (ix) The set of animals on the earth (x) The set of circles passing through the origin (0,0).
Answer» (i) Given set = {1, 2}. Hence, it is finite. (ii) Given set = {2}. Hence, it is finite. (iii) Given set = φ. Hence, it is finite. (iv) We know that there are infinitely many primes. Hence, given set is infinite. (v) There are infinitely many odd numbers. Hence, given set is infinite set. (vi) There are infinitely many parallel lines to the X-axis. Hence, given set is infinite set. (vii) Finite sets (viii) Infinite set (ix) Finite set (x) Infinite set.

State which of the following sets are finite or infinite. (i) {x : x ∈ N and (x – 1)(x – 2) = 0} (ii) {x : x ∈ N and x2 = 4} (iii) {x : x ∈ N and 2x-1 = 0} (iv) {x : x ∈ N and x is prime} (v) {x : x ∈ N and x is odd} (vi) The set of lines which are parallel to the x-axis. (vii) The set of letters in the English alphabet. (viii) The set of numbers which are multiple of 5. (ix) The set of animals on the earth (x) The set of circles passing through the origin (0,0).

Answer»

(i) Given set = {1, 2}. Hence, it is finite.

(ii) Given set = {2}. Hence, it is finite.

(iii) Given set = φ. Hence, it is finite.

(iv) We know that there are infinitely many primes. Hence, given set is infinite.

(v) There are infinitely many odd numbers. Hence, given set is infinite set.

(vi) There are infinitely many parallel lines to the X-axis. Hence, given set is infinite set.

(vii) Finite sets

(viii) Infinite set

(ix) Finite set

(x) Infinite set.