Humans are the intelligent creatures gifted with the ability to reason. Logic and reasoning are very important topics in Mathematics. Inventions have been made by stating mathematical problems and with the help of critical reasoning for their solutions. In this chapter, you will learn in detail about the topics of Mathematical Reasoning.
FAQ on Mathematical Reasoning
Question 1: What is a mathematical statement?
Answer: A mathematical statement refers to the basic unit of any mathematical reasoning. Further, mathematical reasoning is either inductive (mathematical induction) or deductive. Any assertive sentence that can be said to be either true or false but not both means it is a mathematically acceptable statement. Thus, this type of statement is a valid statement.
Question 2: Why is mathematical reasoning important?
Answer: Mathematical reasoning is a very critical skill which allows a student to make use of all other mathematical skills. Thus, people practising mathematical reasoning are able to reflect on solutions to problems and settle on whether or not they are making any sense. They appreciate the pervasive use and power of reasoning as a part of mathematics.
Question 3: What is a contradiction in mathematical reasoning?
Answer: The compound statement that is true for every value of their components is referred to as a tautology. On the other hand, the compound statements which are false for every value of their components are referred to as contradiction (fallacy).
Question 4: What is a compound statement?
Answer: Compound statements are created by combining two or more statements by making use of the connecting words like “and”, “or”, “if, then”, “either, or”, etc. For instance, India is a big and beautiful country is a compound statement.