Final answer:
To write the converse, inverse, and contrapositive of a conditional statement, switch or negate the respective parts. Counterexamples show the invalidity of an argument by presenting cases where premises are true but the conclusion is false.
Step-by-step explanation:
To form the converse of a conditional statement, you switch the hypothesis and conclusion. The inverse is formed by negating both the hypothesis and conclusion of the original conditional. The contrapositive negates and switches the hypothesis and conclusion of the conditional.
For the conditional "If you walk in the rain, your shirt will get wet," the converse would be "If your shirt gets wet, then you walked in the rain," the inverse would be "If you do not walk in the rain, then your shirt will not get wet," and the contrapositive would be "If your shirt is not wet, then you did not walk in the rain." A possible counterexample to the original statement could be that a person's shirt may get wet even if they did not walk in the rain, perhaps due to a sprinkler or another water source.
Counterexamples are scenarios where the premises are true, but the conclusion is false, showing that an argument is invalid.