Which one of the following could be a complete and accurate list of the messages left on the answering machine, from ...
emilymorganizedJuly 25, 2021
Writing out transitive properties
In general, we should not write out the chains linking together our sufficient & necessary conditions/contrapositives because it takes too much time and causes redundant work. Should we just be able to immediately recognize the link between no H / L and no T to an insufficient number of variables? Or does this game present an exception to the rule/guideline, where it is actually helpful to write out the chains?
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...But to add to the chain provided, can't we also conclude that P must leave a message, and therefore the only two who CANNOT leave a message are G or F?
AnneJanuary 25, 2022
I am also wondering why it's stated that H, L, and T must be included, but it's not said that H, L, T, and P must be included?
AbigailJanuary 26, 2022
Hello @emilumorganized and anonymous,
Great questions! The extend to and frequency with which you should be writing out chains depends on many factors (the time you have left, your comfort level with chains, the difficulty of the game, etc.). I personally find it useful to write out the chains most of the time, but I know many tutors who have success writing out the chains less often. Figure out what works best for you. Yes, you are right that we can also conclude that P must leave a message. This is due to the fact that if P was out, then F and G would also be out, and we can only have a maximum of 2 out.
