This is exercise 8.48 from Language, Proof, and Logic 2nd edition. I need help o

Question

This is exercise 8.48 from Language, Proof, and Logic 2nd edition. I need help on this question. I don't know what to do next in order to get the conclusion right. Can anyone help me?

1. Small(a) a (Medium(b) v Large(c)) 2. Medium(b) -> FrontOf(a,b) 3. Large(c) -> Tet(c) 4. Tet(c) 5. -Tet(c) 6. Medium(b) v Large(c) A Elim :1 7. Medium(b) 8. FrontOf(a,b) 9. FrontOf(a,b) v Tet(c) 10. Large(c) 11. Tet(c) 12. FrontOf(a,b) v Tet(c) ? Elim :2,7 v Intro .8 >Elim :3,10 v Intro :11 Elim :10-127-96 13. FrontOf(a,b) v Tet(c) 14.-????) ^ (FrontOf(a,b) v Tet(c)) A Intro :5,13 15. ?Tet(c) ? FrontOf(ab) X ? Elim :5-14 Goals V Mav use intro/elim rules for t/f connectives. May use intro/elim rules for identity. May use intro/elim rules for quantifiers May use full Taut Con. May use Ana Con with literals

Explanation / Answer

here

from the step 5 ~Tet(c) is true

and from step 8 FrontOf(a,b) is true

step 8 is derived from step 2 and 7

now

p -> q is false only when q is false and true in all other cases

hence here instead of using step 14

we can use step 5 and step 8 and join them using ->

as both are true

=> ~Tet(c) -> frontof(a,b ) is true

which is the required conclusiom

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