Question

If A=\left\\{ \dfrac{1}{x}:x\in N\text{ and }x<8 \right\\} and B=\left\\{ \dfrac{1}{2x}:x\in N\text{ and }x\le 4 \right\\} then find:
(a). A – B
(b). B – A

Answer 1

Hint: In order to solve this question, we need to first convert the given sets to their roster form. Now A-B will give us the elements of A which are not common in both A and B , similarly B-A will give us the elements of B which are not common in both.

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 $\cap$ .
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 of the question. First, let us convert set A to roster form. It is given that A=\left\\{ \dfrac{1}{x}:x\in N\text{ and }x<8 \right\\} . So, the possible values of x are 1, 2, 3, 4, 5, 6, 7. Therefore, we can say that set A=\left\\{ \dfrac{1}{1},\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5},\dfrac{1}{6},\dfrac{1}{7} \right\\} .
Now we will convert set B to its roster form. It is given that B=\left\\{ \dfrac{1}{2x}:x\in N\text{ and }x\le 4 \right\\} . So, the possible values of x are 1, 2, 3, 4. Therefore, we can say that set B=\left\\{ \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{6},\dfrac{1}{8} \right\\} .
So, for part (a), we have
A-B=\left\\{ \dfrac{1}{1},\dfrac{1}{3},\dfrac{1}{5},\dfrac{1}{7} \right\\}
Also, for part (b), we have
B-A=\left\\{ \dfrac{1}{8} \right\\}

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. This is a simple question and so the chance of making silly mistakes in a hurry to solve it are also higher.