Symbolize
and provide derivations for each of the following.
1. Mr. A actually is the same
person as Mr. B. Anyone who is clever will escape. Mr. A is
clever. Therefore, we know Mr. B will escape.
a=b, (x)(Cx -> Ex) , Ca |- Eb 1.
a=b 2.
(x)(Cx -> Ex) 3.
Ca
/ show Eb 4.
Ca -> Ea 2, UI 5.
Ea
3,4, MP 6.
Ea -> Eb 1, Id 7.
Eb
5,6, MP
2. Unless there are not at least two individuals who like Don, he
will be elected.. Al likes Don and Bob likes Don, and Al and Bob
are different individuals. Therefore, Don will be elected.
~(Ex)(Ey)[Lxd & Lyd & ~x=y) v
Ed, Lad & Lbd, ~a=b |- Ed 1.
~(Ex)(Ey)[Lxd & Lyd & ~x=y) v Ed 2.
Lad &
Lbd
3.
~a=b
\ show Ed 4.
Lad & Lbd &
~a=b
2,3 Conj I omit additional
grouping since the main connectives are all ampersands 5.
(Ey)(Lad & Lyd &
~a=y)
4, EG 6.
(Ex)(Ey)(Lxd & Lyd & ~x=y)
5, EG 7.
Ed
1,6, DS
