1. Study Questions for Quiz 7 The exam has three parts: 1. (45 pts) Argument Translation in Predicate Logic 2. (65 pts) Proofs and Trees in Predicate Logic 3. (20 pts) Proof in Propositional Logic

2. Study Questions for Quiz 7 1. (45 pts) Argument Translation in Predicate Logic There will be about 3 or 4 arguments to translate. Sample: Translate using the notation provided. Add missing dictionary items in the blanks to the right. Only the gods can take power from me. So no human can take power from me, since No human is a god. _________ god _________ can take power from me _________ human Solution: $x(Cx>Gx) Gx = x is a god -#x(Hx&Gx) Cx = x can take power from me -#x(Hx&Cx) Hx = x is a human

3. Study Questions for Quiz 7 2. (65 pts) Using Proofs and Trees in Predicate Logic Sample: Show valid with a tree and a proof: $x(Mx>-Gx), #x(Bx&Gx) | #x(Bx&-Mx) Tree Solution : Proof Solution: $x(Mx>-Gx) #x(Bx&Gx) -#x(Bx&-Mx) $x-(Bx&-Mx) Ba&Ga Ma>-Ga -(Ba&-Ma) Ba Ga -Ma -Ga -Ba --Ma * * $x(Mx>-Gx) #x(Bx&Gx) -#x(Bx&-Mx) $x-(Bx&-Mx) Ba&Ga Ma>-Ga -(Ba&-Ma) Ba Ga Ba>Ma Ma -Ga Ga&-Ga #x(Bx&-Mx) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) A PA 3 QE 2 #O 1 $O 4 $O 5 &O 7 AR 10,8 >O 6,11 >O 9,12 &I 3-13 -O

4. Study Questions for Quiz 7 3. (20 pts) Propositional Logic Proof Sample: PvQ, -T>-P, T>R, -(Q&-S) | RvS Solution: PvQ -T>-P T>R -(Q&-S) P P>T T R RvS P>(RvS) Q Q>S S RvS Q>(RvS) RvS 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) A PA 2 CN 6,5 >O 3,7 >O 8 vI 5-9 >I PA 4 AR 12,11 >O 13 vI 11-14 >I 1,10,15 vO