|Q1: I have a question about the homework. How would you like us to prove that the propositional equivalences in question 6 hold. Should we do it through truth tables or by showing that the equivalences follow based on other equivalences like the method in example 7 in section 1.3 of the book? Also, if we can prove it using the latter method can we take the rules in tables 6,7 and 8 in section 1.3 as given, rather than proving them, except of course for the rule in table 8 that you're trying to have us establish is valid in question 6a?|
|A1: That's a great question. I had in mind truth tables, but you may certainly do it using the given propositional equivalence, but, of course as you say you may not use the equivalence that you are trying to prove.|
I am a little confused with the "→" notation. I understand how that notation works, but its confusing when it comes to translating "→" to words.
A perfect example is one of the homework problems, number 1.
so w → b translates to
buying a lottery ticket is necessary for winning the jackpot.
and winning the million dollar jackpot is sufficient for buying the ticket. right?|
To me, necessary=sufficient. Can you elaborate.
|A1: Thanks for your question. Sufficient means enough. We say that "w is a sufficient condition for b" if making sure that w is true is enough to make sure that b is true, i.e., w → b. We say that b is necessary for w if b must be true in order for w to be true, i.e., whenever w is true, b must be true, i.e., w → b. I hope this helps.|