Question: Show that the set of letters needed to spell “LUMINIOUS“ and the set of letters needed to spell “ MU...

Question

Show that the set of letters needed to spell “LUMINIOUS“ and the set of letters needed to spell “ MUSULION “ are equal.

Answer 1

Solution

In order to solve this question, we need to first convert the given sets to their roaster form. Then you need to compare the pair of sets to check whether they are equal or not.

Complete step-by-step solution:
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 $\cap$ .
Two sets are said to be equal if they have the all there elements equal.
Now let us move to the solution of the above question. We let the set of letters needed to spell “LUMINIOUS” be set A and the set of letters needed to spell “MUSULION” be set B.
Let us convert set A to roster form. It is given that $A=\\{x:x\text{ is a letter of the word ''LUMINIOUS''}\\}$ . So, the possible values of x are L, M, I, N, U, O, S. Therefore, we can say that the set $A=\left\\{ L, M, I, N, U, O, S \right\\}$ .
Now we will convert set B to its roaster form. It is given that $B=\\{x:x\text{ is the letter of the word ''MUSULION''}\\}$ . So, the possible values of x are M, U, S, L, I, O, N. Therefore, we can say that the set $B=\left\\{ M, U, S, L, I, O, N \right\\}$ . Hence, set A is equal to set B.
Therefore, we have shown that the set of letters needed to spell “LUMINIOUS“ and the set of letters needed to spell “ MUSILION “ are equal.

Note: We have used the fact that when the two sets are said to be equal, 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.