Consider the following statement:
“All mathematicians must be good logicians and all good logicians must justify their claims.”
a) Write this statement symbolically as a conjunction of two conditional statements. Use three components (p, q, and r) and explicitly state what these are in your work. Remember: a component in logic is a simple declarative sentence that is either true or false.
b) Write the negation of this statement
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Okay, so suppose we have the form: "All p must be q". The question is does this mean \(p\implies q\) or \(q \implies p\)? You have to test it out a bit.
So I'd start out with something like... "All dogs must be animals". Now does this mean "If you're a dog, then you're an animal." or does it mean "If you're an animal, you must be a dog"?