What is Mathematical Reasoning?
In mathematics, there are two different kinds of reasoning :
- Inductive Reasoning
- Deductive Logic Reasoning.
Logic is the study that is done with the method of reasoning. Along with proving the theorem, it provides us with the rules for determining the validity of a given argument.
Also Read: Principle of mathematical induction
What is Statement (Proposition)?
The basic unit involved in mathematical reasoning is a mathematical statement
A statement is an assertive sentence which is either true or false but not both a true statement is called a valid statement. Otherwise, it is called an invalid statement.
Denotion of Statement
Statements are denoted by the small letters i.e., p, q, r … etc.
- Mathematics is fun.
- This sentence is subjective in the sense that for those who like mathematics, it may be fun but for others, it may not be. This means that this sentence is not always true. Hence it is not a statement.
- A statement should be a “mathematically acceptable” statement
- An ambiguous sentence is not acceptable as a statement in mathematics.
Methods to Check Validity
We can use various methods to check the validity of a statement such as:
- Direct Method
- Contrapositive method
- Methods using contradiction
- Methods using counterexample
Also Refer: Mathematical Reasoning and Statements