Question

Applied discrete maths, please explain if its true or false use

of the rule of inference.
if it is rain today, i watch a movie. i did not watch a movie
today therefore it did not rain today.

Answer 1

The inference made by the student is an example of 'denying the antecedent,' which is an invalid argument form and does not necessarily lead to a true conclusion, even if the premises are true.

Step-by-step explanation:

The student's question refers to a logical inference known as denying the antecedent. This type of inference is generally regarded as an invalid argument form. In the given example, the premise is 'If it rains today, I watch a movie.' The student then states, 'I did not watch a movie today,' and concludes 'Therefore, it did not rain today.' This is a fallacy because not watching a movie does not necessarily imply that it did not rain. There could be other reasons for not watching a movie despite the occurrence of rain. This is different from modus tollens, where the valid logical form would be 'If it rains, I watch a movie. It did not rain, therefore, I did not watch a movie.'