Question

Which of the following regarding null sets are correct.
Empty set is considered as subset of all sets
Union of an empty set $\phi $with a set X is an empty set
Intersection of an empty set with a set X is x.
A) (ii) and (iii)
B) (i) only
C) (i) and (ii)
D) (i), (ii) and (iii)

Answer 1

Hint: Set can be defined as the collection of the distinct objects or the elements which have common property. Here we will understand the given multiple statements and choose the correct options.

Complete step by step solution:
Empty set is considered as subset of all sets
I.A set is known as the subset of itself since any set contains all its elements. Also, an empty set which is also known as the null set is the subset of every set because every element in the empty set belongs to any set since the empty set contains no elements.

(II) Union of an empty set $\phi $with a set X is an empty set
Union of any empty set and set X gives set X, so the given statement is not true.

(III) Intersection of an empty set with a set X is x.
Intersection means the elements common in both the sets, so the intersection between an empty set and X gives an empty set and hence the given statement is false.
From the given multiple choices, option B is the correct answer.
So, the correct answer is “Option B”.

Note: Set builder notation is used to define a set by numbering the elements or stating the properties to satisfy for its members. Always know the difference and co-relation between the types of sets. Follow the given conditions properly while converting the set-builder to roster form and check it twice. Union between the sets are the elements from both the sets, it may be in one or all the sets while intersection of the sets gives the elements common in all the sets.