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When I cover the topic, no one ever is confused by T -> F. For the others, I have an example (in the metalanguage, obviously). Consider "if a number is prime
by jimhefferon 9y ago
When I cover the topic, no one ever is confused by T -> F. For the others, I have an example (in the metalanguage, obviously).
Consider "if a number is prime then it isn't a perfect square." Should be true, right? If you can't split it then you can't split it into equal parts.
Now take the number to be 6. That suggests that F -> T should evaluate to T.
Take the number to be 4. That suggests F -> F is T.
And 3 suggests what to do with T -> T.
- fizixer 9y agoYour example makes sense but at the same time it's something I like to call "a positive example". If you explain it to new students, they would agree with you and would think they understand material implication. But later if you test their knowledge using one of the counter-intuitive examples, more often than not, they would have a hard time reconciling it with their understanding. (e.g, the one that I posted here: https://news.ycombinator.com/item?id=15115319 https://news.ycombinator.com/item?id=15115319).
- jimhefferon 9y agoPeople don't learn things by being told them. For anything that is hard, they learn by gradual approximation.