# Logical Proofs

Logical Proofs

For the following interactive exercises, you will be asked to

complete a proof. For each line that you add to your proof, you will need to justify its derivation by notating the relevant preceding line(s) and rule of inference, until you reach the conclusion on a line by itself.

Refer to the fold-out card at the end of Baronett, Logic, 3rdedition, for the following argument forms:

· The Eight Implication Rules

· The Ten Replacement Rules

· Inference Rules for Predicate Logic

SFor the following interactive exercises, you will be asked to
complete a proof.For each line that you add to your proof, you will need to justify its derivation by notating the relevantpreceding line(s)and rule of inference, until you reach the conclusion on a line by itself.
Refer to the fold-out card at the end of Baronett, Logic, 3rdedition, for the following argument forms:
• The Eight Implication Rules
• The Ten Replacement Rules
• Inference Rules for Predicate Logic

Create a proof for the following argument. Show 3 possible outcomes (if applicable) for the missing line.

#1
1. (M ? R) ?~K
2. (G ?~K) ? C
3.G ? (M ? R) /C
4. ?

#2
1. (H ? M) ? L
2.L ? H
3.H ? (M ? H)
4.~(M ? H) /M
5. ?

#3
1. M ? H
2.(K ? F) ? M
3.K /H
4. ?

#4
1. (C ? K) ? L
2.~B ?~H
3.(~B ? F) • (~H ?~A)
4.(F ?~A) ?~L /~(C ? K)
5. ?

#5
1. F • ~C
2.(B • G) ? (C • D) /~(B • G)
3.?
#6
1. (x)~Qx
2.(x)[(Sx ? Px) = Qx] /(x)(Px = Sx)
3. ?

#7
1. (x)(Px ? Sx)
2.(x)(Px ? Qx) /(x)[Px ? (Qx • Sx)
3. ?

#8
1. (x)(y)(Jxy ? Kxy)
2.~Kcb /~Jcb
3. ?

#9
1. (z)(Fz ? Gz)
2.~Gb
3.a = b /~Fa
4. ?

#10
1. (?x)(Fx • Mx)
2.(x)(x = b) /Mb
3. ?