Question

Which of the following is the correct steps to take when proving a statement using proof by contradiction?

• A. 1) Assume that your statement is true.
  2) Show this is the case using definitions and theorems.
  3) State that the statement is true.
• B. 1) Assume your statement is true for a certain instance.
  2) Show that it is true in more than one instance.
  3) State that your statement must be true.
• C. 1) Assume your statement to be false.
  2) Proceed as you would in a direct proof.
  3) Come across a contradiction.
  4) Use the contradiction to state that your assumption of the statement being false can't be the case, so your statement must be true.
• D. None of the answers are correct.

Answer 1

The correct option is C 1) Assume your statement to be false.

2) Proceed as you would in a direct proof.
3) Come across a contradiction.
4) Use the contradiction to state that your assumption of the statement being false can't be the case, so your statement must be true.
Proof by contradiction can be used to prove any kind of statements.

Steps to be followed:

$\to$ Assume the statement we want to prove to be false.

$\to$ Then start proving from that statement.

$\to$ We end up seeing our assumption to be wrong.

$\to$ Now we can conclude our statement to be true.