Table of Contents
Exercise 2.4 Solutions – Class X Mathematics
These solutions are based on the Telangana State Class X Mathematics textbook, focusing on set properties and cardinality. Mathematical expressions are rendered using MathJax.
1. State which of the following sets are empty and which are not?
(i) The set of lines passing through a given point.
Infinite lines pass through any given point (e.g., in a plane).
Conclusion: Not empty
(ii) Set of odd natural numbers divisible by 2.
No odd number is divisible by 2 (odd numbers are not even).
Conclusion: Empty
(iii) {x : x is a natural number, x < 5 and x > 7}
No natural number satisfies both x < 5 and x > 7 simultaneously.
Conclusion: Empty
(iv) {x : x is a common point to any two parallel lines}
Parallel lines do not intersect, so no common point exists.
Conclusion: Empty
(v) Set of even prime numbers.
The only even prime number is 2.
Conclusion: Not empty
2. State whether the following sets are finite or infinite.
(i) The set of months in a year.
There are 12 months in a year, a fixed number.
Conclusion: Finite
(ii) {1, 2, 3, …, 99, 100}
Contains 100 elements, a fixed number.
Conclusion: Finite
(iii) The set of prime numbers smaller than 99.
Finite number of primes less than 99 (e.g., 2, 3, 5, …, 97).
Conclusion: Finite
(iv) The set of letters in the English alphabet.
Contains 26 letters, a fixed number.
Conclusion: Finite
(v) The set of lines that can be drawn are parallel to the X-Axis.
Infinite lines can be drawn parallel to the X-Axis in a plane.
Conclusion: Infinite
(vi) The set of numbers which are multiples of 5.
Multiples of 5 are infinite (5, 10, 15, …).
Conclusion: Infinite
(vii) The set of circles passing through the origin (0, 0).
Infinite circles can pass through the origin with different radii.
Conclusion: Infinite
