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.