Final answer:
The syllogism 'If I take swimming lessons, I can swim. I cannot swim. Therefore, I did not take swimming lessons' which is an example of modus tollens.
Step-by-step explanation:
The type of syllogism presented in the question is modus tollens. This form of logical argument uses a conditional statement where the first premise provides that one statement is sufficient for another, as in 'if X, then Y'. The second premise of modus tollens asserts the negation of the consequent, 'not Y'. The conclusion logically drawn from these premises is the negation of the antecedent, 'not X'. In the given syllogism: 'If I take swimming lessons, I can swim. I cannot swim. Therefore, I did not take swimming lessons, we are indeed using modus tollens, because the inability to swim ('not Y') leads to the conclusion that the person did not take swimming lessons ('not X').