### Sets Class 10th Mathematics AP Board Solution

##### Question 1.State which of the following sets are empty and which are not?(i) The set of lines passing through a point.(ii) Set of odd natural numbers divisible by 2.(iii) {x : x is a natural number x < 5 and x > 7}(iv) {x : x is a common point to any two parallel lines}(v) Set of even prime numbers.Answer:We know that an empty set is a finite set. A set which does not contain any element is called an empty set.(i) Let ‘L’ be the set of lines passing through a point. Then L is infinite. So, it is not an empty set.(ii) Let ‘O’ be the set of odd natural numbers divisible by 2.But only even numbers are divisible by 2.∴ O = ϕ = Empty set(iii) {x: x is a natural number x < 5 and x > 7}⇒ If x < 5 and x > 7, then⇒ x = ϕ = Empty Set(iv) {x : x is a common point to any two parallel lines}We know that two parallel lines do not intersect. So, there is no common point.∴ x = ϕ = Empty set(v) Set of even prime numbersLet ‘E’ be the set of even prime numbers.⇒ E = {2} ≠ ϕ∴ It is not an empty set.Question 2.Which of the following sets are finite or infinite.(i) The set of months in a year.(ii) {1, 2, 3, …, 99, 100}(iii) The set of prime numbers smaller than 99.Answer:We know that a finite set is the set in which the number of elements of the set are finite and an infinite set is the set in which the number of elements of the set are not finite.(i) Let ‘M’ be the set of months in a year.∴ M = {January, February, March, April, May, June, July, August, September, October, November, December}There are 12 elements in ‘M’.∴ ‘M’ is finite.(ii) {1, 2, 3 … 99, 100}There are 100 elements in the above set.∴ The given set is finite.(iii) Let ‘P’ be the set of prime numbers less than 99.⇒ P = {2, 3, 5, 7, 11 … 89, 97}There are 25 elements i.e. prime numbers less than 99.∴ P is finite.Question 3.State whether each of the following sets is finite or infinite.(i) The set of letters in the English alphabet.(ii) The set of lines which are parallel to the X-Axis.(iii) The set of numbers which are multiplies of 5.(iv) The set of circles passing through the origin (0, 0).Answer:We know that a finite set is the set in which the number of elements of the set are finite and an infinite set is the set in which the number of elements of the set are not finite.(i) Let ‘E’ be the set of letters in the English alphabet.⇒ E = {A, B, C, D … X, Y, Z}There are 26 alphabets.∴ E is a finite set.(ii) Let ‘L’ be the sets of lines which are parallel to X-axis.Then L is an infinite set.(iii) Let ‘M’ be the set of multiples of 5.⇒ M = {5, 10, 15, 20 …}∴ M is an infinite set.(iv)Let ‘S’ be the set of circles passing through the origin (0, 0).Then S is an infinite set.

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