Question

In an indirect proof by contraposition, the first step is to __________.

A. assume the conclusion, or q, is false
B. show that the assumption leads to a contradiction
C. assume the hypothesis, or p, is false
D. show that a definition or theorem proves the hypothesis correct

Answer 1

In an indirect proof by contraposition, the first step is to assume that the hypothesis, or p, is false. Counterexamples are used to validate the arguments by checking for situations where premises are true but the conclusion is false which thus demonstrates the invalidity of the argument.

Step-by-step explanation:

In an indirect proof by contraposition, the first step is to assume the hypothesis, or p, is false. This technique is used in deductive reasoning where if a conditional statement is to be proven, and it is of the form 'if p then q', contraposition allows us to consider the equivalent statement 'if not q then not p'. If we can show that assuming not q leads to the truth of not p, the original conditional statement is supported.

To apply this proof method effectively, counterexamples can be vital. A counterexample in a logical argument is a situation in which all the premises are true, but the conclusion is false. This helps identify weak points in an argument or claim, providing a means of testing for invalidity. Also, when assessing the truth in the premises of an argument, one should consider potential counterexamples to the claim made within the premise for a more robust philosophical or logical analysis.