Question

Let A = $\\{x:x\,\text{is a letter of the word }\\!\\!'\\!\\!\text{ paper }\\!\\!'\\!\\!\text{ }\\!\\!\\}\\!\\!\text{ }$ and B = set of digits in the number 59678. Then set A and B are equal.
(a) True.
(b) False.

Answer 1

Hint: In this question, we will use equality of two sets to compare both the given sets. Hence, we can find answers to the given question.

Complete step-by-step answer:
Set is a collection of well-defined elements, where elements can be anything like numbers, letters, words, etc.
Now, we can write a set in two forms namely tabular form and set-builder form.
In tabular form, all the elements of the set are written within the braces { }. Different elements within the set are separated by commas.
Example, {1,2,3,4}.
In set-builder form, the element or element of the set are defined such that all the elements in the set possess that property and no other element outside the set have that property. In this form, within the braces { }, we first write the variable which is used for all the elements of the set and then give colon and after the colon we write definition of the elements of the set.
Example, {$x:x$ is an integer between 0 and 5}.
Now, two sets are said to be equal, if all the elements of both the set are equal, irrespective of the order in which they are written. And there is no other element other than the equal elements.
Example, {1,2,3,4} is equal to {2,4,3,1} but {1,2,3,4} is not equal to {1,2,3,4,5}.
Now, let us write the sets given in questions in tabular form as below,
A = {p, a, p, e, r} = {p, a, e, r}.
And, B = {5, 9, 6, 7, 8}.
Here, as we can see, elements of A are letters whereas elements of B are numbers. So, we cannot compare the elements of both the sets. Therefore, the elements of A are not equal to the elements of B.
Hence, we can say that A is not equal to B.
Therefore, the correct answer is option (b).

Note: Whenever the elements of two or more different set are of different types such that their comparison is not possible. In such cases, those sets can never be equal.