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)