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Homework 2 Solution
p.22 Problem B:
3. necessarily true because the property of being "good building material" is the same as being "useful for building things"
4. necessarily false because a three story building cannot be only two stories tall
5. contingent because its truth depends on the definition of "mammal", which could change
p.22 Problem C:
2. not necessarily equivalent -- the first sentence is a universal statement about all mammals while the second is a conditional about one particular mammal
3. not necessarily equivalent -- they have nothing to do with each other (in as much as logic is concerned)
4. necessarily equivalent -- being "44th" means by definition you are immediately after "43rd"
p.22 Problem F:
1. impossible because if M2 holds, then M1 says Socrates is mortal, but M3 says Socrates is not mortal
3. jointly possible (if immortal people existed)
4. jointly possible
p.22 Problem G:
2. possible -- if the premises are false, then it is impossible to devise a counterexample, meaning the argument would be considered valid
Example: "Pafnuty is three years old. Pafnuty is two years old. $\therefore$ Three is bigger than five."
5. impossible -- being contingent means it could be either true or false but being a necessary truth means it must always be true
8. possible -- being necessarily equivalent just means their truth values match and being jointly impossible means it is not possible for them to both be simultaneously true
Example: "First sentence: $2=3$, Second sentence: $3=4$."
10. possible -- jointly impossible just means that all cannot be true simultaneously, but this does not rule out one of them being true all of the time
Example: "First sentence: $1=1$, Second sentence: $0=1$"