# AP Board 9th Class Maths Notes Chapter 15 Proofs in Mathematics

Students can go through AP Board 9th Class Maths Notes Chapter 15 Proofs in Mathematics to understand and remember the concepts easily.

## AP State Board Syllabus 9th Class Maths Notes Chapter 15 Proofs in Mathematics

→ The sentences that can be judged on some criteria, no matter by what process for their being true or false are statements.

→ Mathematical statements are of a distinct nature from general statements. They cannot be proved or justified by getting evidence while they can be disproved by finding a counter example.

→ Making mathematical statements through observing patterns and thinking of the rules that may define such patterns.
A hypothesis is a statement of idea which gives an explanation to a sense of observation. → A process which can establish the truth of a mathematical statement based purely on logical arguments is called a mathematical proof.

→ Axioms are statements which are assumed to be true without proof.

→ A conjecture is a statement we believe is true based on our mathematical intuition, but which we are yet to prove.

→ A mathematical statement whose truth has been established or proved is called a theorem.

→ The prime logical method in proving a mathematical statement is deductive reasoning.

→ A proof is made up of a successive sequence of mathematical statements.

→ Beginning with given (Hypothesis) of the theorem and arrive at the conclusion by means of a chain of logical steps is mostly followed to prove theorems. → The proof in which, we start with the assumption contrary to the conclusion and arriving at a contradiction to the hypothesis is another way that we establish the original conclusion is true is another type of deductive reasoning.

→ The logical tool used in the establishment of the truth of an un-ambiguous statement is called deductive reasoning.

→ The reasoning which is based on examining of variety of cases or sets of data discovering pattern and forming conclusion is called Inductive reasoning.