Question

If R is the set of all real numbers and Q is the set of all rational numbers, then what is set (R-Q).

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 Q is the subset of R if and only if all the elements of set Q are present in set R.

Complete step-by-step answer:

Before starting with the solution, let us discuss different symbols and operations related to the above question.
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. Real numbers are those numbers which can be represented on a number line, i.e., the union of rational and irrational number is the set of real numbers, while rational numbers are those real numbers that can be written in the form of $\dfrac{p}{q}$ such that both p and q are integers and $q0$ . In other words, we can say that the numbers which are either terminating or recurring when converted to decimal form are called rational numbers. So, we can say that $Q\subset R$ , so we can say that all the terms of Q are present in set R. Also, we know that R-Q represents the set which contains all the terms of R which is not present in Q. Therefore, the set R-Q represent the set of irrational numbers.
Hence, the answer to the above question is a set of irrational numbers..

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.