Understanding Symbolic Logic, Virginia Klenk, Pearson Prentice Hall, 5th edition, 2008, Unit 20, Ex. 1(a)

Once again we have to prove the argument. Unlike in the Mandy Andy argument in an earlier post, the conclusion here accords with our intuition.

The sports car buff who owns a Maserati is unemployed. Mary is a sports car buff and owns a Maserati. So, Mary is unemployed.

1. (∃x){Bx • Mx • (y)[(By • My)⊃y = x] • ¬ Ex}
2. Bm • Mm
3. ∴¬ Em
4. Ba • Ma • (y)[(By • My)⊃y = a] • ¬ Ea ......... 1EI x/a
5. (y)[(By • My)⊃y = a] ......... 4Simp.
6. (Bm • Mm)⊃m = a ......... 5UI y/m
7. m = a ......... 2,6MP
8. ¬ Ea ......... 4Simp.
9. ¬ Em ......... 7,8Id