Exercise 2.4
1. State which of the following sets are empty and which are not?
The set of lines passing through a given point.
Set of odd natural numbers divisible by 2.
x : x is a natural number, x < 5 and x > 7
x : x is a common point to any two parallel lines
Set of even prime numbers.
Empty
Not Empty
2. State whether the following sets are finite or infinite.
The set of months in a year
1, 2, 3, ..., 99, 100
The set of prime numbers smaller than 99.
The set of letters in the English alphabet.
The set of lines that can be drawn parallel to the X-Axis.
The set of numbers which are multiples of 5.
The set of circles passing through the origin (0, 0).
Finite
Infinite
If A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8} then find n(A ∪ B).
Solution:
Given: A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}
Count elements in each set: n(A) =
Find A ∪ B: A ∪ B represents
Count elements in A ∪ B: n(A ∪ B) =
Verification: Using n(A ∪ B) = n(A)
So, n(A ∩ B) =
Answer: A ∪ B contains only 7 elements, not 9, because the elements