The concept of mathematical reasoning helps in deciding whether the given statement is correct or wrong. It is mainly dependent upon the statement. We can define mathematical reasoning as the logic used to know either the statement is true or false. This concept is widely used in competitive examinations as it helps to test the knowledge and thinking capacity of the brain of each individual.
Statements are the fundamental factors in mathematical reasoning. The most important condition for a statement is that it can only be a true statement or a false statement. But it must not be true and false in the same instant.
Let’s consider an example to understand this well.
STATEMENT: Asia is a continent.
In the above statement, Asia is truly a continent. So the statement is true. Hence, it is considered a mathematical statement.
STATEMENT: The product of two irrational numbers is rational
The product of two irrationals may be rational sometimes and also irrational in some cases. The given statement is both true and false at once. Hence, it can’t be considered a mathematical statement.
Inductive reasoning is obtained by one’s observations. These observations give you a conclusion on your consideration and help in creating generalizations. However, your conclusion may or may not be true all the time.
Whereas, deductive reasoning is a contradiction to inductive reasoning. In deductive reasoning, we use general principles to conclude. It is mostly applied the reasoning in many fields. Example: marketing, etc.
Statement 1: A school is a place of learning.
Statement 2: Everyone has to go to school.
Since school is a place of learning, everyone has to go to school for learning. So, statement 1 is proved to be true. Therefore, statement 2 is also true.
Note that both of the statements are dependent on each other.
To find out the result for the given statements, we use some methods which help in the correct conclusion of the statement.
But this contradicts the fact that √3 is irrational.
Hence,4/5√3 is an irrational number.