Question

If A and B are two sets such that $A\subseteq B$ then find A-B.

Answer 1

Hint: To solve the above question, you need to apply the definition of the subsets and also the knowledge related to the subtraction of two sets. Remember that A is the subset of B if and only if all the elements of set A are present in set B.

Complete step-by-step answer:

Before starting with the solution, let us discuss different symbols and operations related to sets.
Union: The union (denoted by $\cup $ ) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
Intersection: The intersection of two sets has only the elements common to both sets. If an element is in just one set it is not part of the intersection. The symbol is an upside down $\cap $ .
Subset: A set A is said to be the subset of set B, if all the terms of A are present in set B, i.e., set A is contained in set B. This can be represented as: $A\subset B$ .
When we subtract two sets the common elements of the set which is being subtract is removed, and the remaining elements is the final answer.
Now let us start with the solution to the question. As it is given in the question that $A\subseteq B$ , so we can say that all the terms of A are present in set B. Also, we know that A-B represents the set which contains all the terms of A which is not present in B, but as all the terms of A are present in set B, the set A-B is a null set.
Hence, the answer to the above question is null set or $\phi $ .

Note: We have used the fact that how the two sets are subtracted, and also the definition of the given terms are also useful. One must memorize the definition so that there can be no mistake in the future. Null sets are also called empty sets, that is there are no number of elements present in it.