Final answer:
The phrase provided by the student is not a logical statement type. Conditional statements are formulated as 'if-then' and a counterexample is a particular instance that disproves a general statement.
Step-by-step explanation:
The student's question, 'If only 5 doctors were asked about their opinion of new medicine,' does not represent a logical statement type, such as a conditional, biconditional, inverse, or contrapositive statement. Instead, it seems to be an incomplete statement that does not imply any logical condition or consequence. It may simply be a preface to a question about a survey or consensus.
Conditional statements are commonly expressed in the form 'if A, then B,' indicating that B is a necessary consequence of A. An example of a conditional statement would be, 'If it rains, the ground will get wet.' When considering the nature of logical statements, it is important to understand their structure and meaning in the context of logic.
To define an inverse statement, one negates both the hypothesis and the conclusion. For example, the inverse of 'If it is raining, then the ground is wet' would be 'If it is not raining, then the ground is not wet.'
A contrapositive statement involves reversing and negating both the hypothesis and the conclusion of a conditional statement. Using our example, the contrapositive would be 'If the ground is not wet, then it is not raining.'
A counterexample is an instance that refutes a general statement by showing that despite the conditions being met, the conclusion does not follow. For example, a counterexample to the conditional statement 'If you walk in the rain, your shirt will get wet' could be someone walking in the rain with an umbrella, preventing the shirt from getting wet.