I've used this quick 10 question quiz (with the answer key included) to assess student understand of basic If A=B and B=C then A=C logical relationships. This works great as a quick 10 minute quiz to measure student understanding of logic before moving on to the more complex idea of logical fallacies.
I've included the directions below so you can see what students are asked to do:
Directions: For each syllogism, decide whether the conclusion follows the premises (the major and minor statement). If the conclusion does logically follow the premises, just write “True” on the lines. If the syllogism does not logically follow from the premises, rewrite the conclusion on the lines so the syllogism makes a valid, or true, conclusion.