(i) {1, 2, 3, 6} (a) {x : x is prime number and a divisor of 6}
(ii) {2, 3} (b) {x : x is an odd natural number smaller than 10}
(iii) {m, a, t, h, e, i, c, s} (c) {x : x is a natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}
2.3 EMPTY SET
Let us consider the following examples of sets:
(i) A = {x : x is a natural number smaller than 1}
(ii) D = {x : x is a odd number divisible by 2}
How many elements are there in sets A and D? We find that there is no natural number
which is smaller than 1. So set A contains no elements or we say that A is an empty set.Similarly,
there are no odd numbers that are divisible by 2. So, D is also an empty set.
A set which does not contain any element is called an empty set, or a Null set, or a void
set. Empty set is denoted by the symbol ∅ or { }.
Here are some more examples of empty sets.
(i) A = {x : 1 < x < 2, x is a natural number}
(ii) B = {x : x2
– 2 = 0 and x is a rational number}
Note : ∅ and {0} are two different sets. {0} is a set containing an element 0 while ∅ has no
elements (null set).
2.4 UNIVERSAL SET AND SUBSET
Consider the teeth set that we have discussed in the
begining of the chapter. You have classified the whole teeth
set into four sets namely incisors, canines, premolars and
molars.
But, are teeth in the set of molars also members of whole
teeth set? or not?
Here, whole teeth set is "universal set" of above said four teeth sets.