Question

Which of the following best describes an indirect proof? use definitions and postulates to deduce a conclusion. just accept a statement as true. assume a statement true and then show it must be false.

Answer 1

Answer: (c) Assume a statement is true and show that it must be false.

Step-by-step explanation: In mathematics, particularly in geometrical proofs, we apply different methods to prove a theorem or a result. For example-

(i) Sometimes, we use existing definitions and postulates to arrive at a conclusion. This is a type of direct method of proof, and so, option (a) is incorrect.

(ii) Accepting a statement to be true is not a part of the proof. So, option (b) will also not work.

(iii) First assuming a particular statement to be true and then showing it to be false (arriving at a contradiction) is a type of indirect proof. We call it the method of contradiction.

Thus, the correct option is (c).

Answer 2

Assume a statement true and then show it must be false. 

This is also called 'proof by contradiction'.