7.3h
More Help Thinking About Categorical Logic

Think about this interpretation when doing these derivations.

UD: animals
Wx: x is a whale, Mx: x is a mammal, Fx: x is a fish, Hx: x is happy.
s: Shamu (the killer whale)
u: Ursula (the spider)

So, when you see '(^x)(Wx>Mx)' think "all whales are mammals". The rules are here.



Justification:       Sentence:       

Problem Four.
Premise 1 (^x)(Wx>Mx)
Premise 2 ~(%x)(Mx&Fx)
2 QN 3 (^x)~(Mx&Fx)
3 ^E 4 ~(Ma&Fa)
4 DM 5 ~Ma v ~Fa
5 IM 6 Ma>~Fa
1 ^E 7 Wa>Ma
6,7 HS 8 Wa>~Fa
8 ^I 9 (^x)(Wx>~Fx)
Problem Five.
Premise 1 (^x)(Wx>Mx)  
Premise 2 (%x)(Wx&Hx)  
Assumption 3 ....what if ~(%x)(Mx&Hx)
3 QN 4 ....then... (^x)~(Mx&Hx)
4 ^E 5 ....then... ~(Ma&Ha)
5 DM 6 ....then... ~Ma v ~Ha
6 IM 7 ....then... Ma>~Ha
1 ^E 8 ....then... Wa>Ma
7,8 HS 9 ....then... Wa>~Ha
9 ^I 10 ....then... (^x)(Wx>~Hx)
2 DN 11 ....then... ~~(%x)(Wx&Hx)
11 QN 12 ....then... ~(^x)~(Wx&Hx)
12 DM 13 ....then... ~(^x)(~Wx v ~Hx)
13 IM 14 ....then... ~(^x)(Wx>~Hx)
3-14RD 15 (%x)(Mx&Hx)