Question

Find the number of elements in set A-B

Answer 1

Hint: In this question we have to find the number of elements in set A and B. We know that the number of elements in combining both sets is called union of sets and hence we need to find the number of elements in the union of both the sets. To find union we will create a Venn diagram showing all elements of A and B. And analyse where it lies.
We know that,
\[A\bigcup B\Rightarrow \] Contains all elements in either set
\[A\bigcap \bar{B}\Rightarrow \] all the elements of A which are not in B

Complete step-by-step answer:
Given Venn diagram

We can see that by this diagram
\[\begin{gathered}
  A = \left\{ {a,d,b,e} \right\} \\
  B = \left\{ {c,f,b,e} \right\} \\
  A \cap b = \left\{ {b,e} \right\} \\
  A \cup b = \left\{ {a,b,c,d,e,f} \right\} \\
\end{gathered} \]
Now we have to solve A-B
A-B means all the elements of ‘A’ which are not in B set.
B and c are common in set ‘A’ and set ‘B’ so we cannot write them in A-B
So, we write only a and d
i.e. \[A - B = \left\{ {a,d} \right\}\]

Hence, the number of elements in set A-B is \[\left\{ {a,d} \right\}\]

Note: In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets, whose intersection is the empty set.
In this question ‘g’ and ‘h’ are those elements who are neither the element of set A nor set B.