Students can practice TS 10th Class Maths Solutions Chapter 2 Sets Ex 2.4 to get the best methods of solving problems.
TS 10th Class Maths Solutions Chapter 2 Sets Exercise 2.4
Question 1.
State which of the following sets are empty and which are not ?
a) The set of straight lines passing through a point.
b) Set of odd natural numbers divisible by 2.
c) {x : x is a natural number, x < 5 and x > 7}
d) {x : x is a common point to any two parallel lines}
e) Set of even prime numbers.
Answer:
a) The number of straight lines passing through a point is infinite. So, the given set is non-empty.
b) We know the odd natural numbers are 1, 3, 5, 7,…. are not divisible by 2. Hence the given set is empty.
c) There is no natural number satisfying the given condition. Hence the given set is empty.
d) There is no common point to any two parallel lines because they do not meet when produced on either side. Hence the given set is empty.
e) 2 is the only even prime number. Therefore the set contains one element. Hence the given set is non-empty.
Question 2.
Which of the following sets are finite or infinite ?
a) The set of months in a year.
b) {1, 2, 3,…….., 99, 100}
c) The set of prime numbers less than 99.
Answer:
a) There are 12 months in a year. The set of months in a year contains 12 elements. Hence the set is finite.
b) Obviously, the given set contains 100 elements. Hence the set is finite.
c) We can count the prime numbers less than 99. Hence the set is finite.
Question 3.
State whether each of the following sets is finite or infinite.
a) The set of letters in the english alphabet.
b) The set of lines which are parallel to the x – axis.
c) The set of numbers which are multiples of 5.
d) The set of circles passing through the origin (0, 0).
Answer:
a) The set of letters in the english alphabet contains 26 elements. Hence, the set is finite.
b) We cannot count the number of parallel lines drawn to the x – axis. Hence the set is infinite.
c) The set of numbers which are multiples of 5 is {5, 10, 15, 20, 25, …}. Hence the set contains infinite number of elements. Hence, the set is infinite.
d) The number of circles that can be drawn through the origin (0, 0) is countless. Hence the set is infinite.