# Project #65738 - LOGIC

SEE ATTACHED FILE

Along with these proofs I need the valid argument form, rule or equivalence and state the step that justifies each step. Such as the steps written to the side and the rules usedÃ‚Â

here is an EXAMPLE:

1)B&A Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p

2)C->A Ã‚Â  Ã‚Â  Ã‚Â  p/:~C

3)~A Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  1,simp

4)~C Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  2,3 MT

Ã‚Â

Here are the ACTUAL PROBLEMS i need solved in the same form as above.

2

1) A->~B Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p

2) L -> (A&B) Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p/:~L

Ã‚Â

3

!) (A&~C) v B Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p

2) (B v~C) -> H Ã‚Â  Ã‚Â  Ã‚Â  p/:H

Ã‚Â

4

1) HvH Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  p

2) (M&N) -> ~(HvT) Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  p/: M->~N

Ã‚Â

5Ã‚Â

1) (MvP) v (E&L) Ã‚Â  Ã‚Â  Ã‚Â p

2) H&~P Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p/: ~(~M&~L)

(NOTE: This one is tough, use IP)

Ã‚Â

Ã‚Â

State the rule, valid argument form or equivalence that justifies each step of the following proofs and list the line or lines from which each step is derived.

1

1) Av~(B&C) Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p

2) H&C Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  p/: B->A

3) Av (~Bv~C) Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â 1, DeM

4) (Av~B) v~C Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â Ã‚Â

5) C

6) Av~B

7) ~BvA

8) B->A

Ã‚Â

2

1) C <-> (M->K) Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p

2) M&~K Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â  Ã‚Â p/:~C

3) [C-> (M->K)] & [(M->K)->C] Ã‚Â  Ã‚Â 1,bicon

4) C-> (M->K)

5) (C&M)->K

6)~K

7) ~(C&M)

8) ~Cv~M

9) M

10) ~C

Ã‚Â

~= Not, negation

&=and

v= or

->= if then, conditional

<->= if and only if, biconditional

 Subject Philosophy Due By (Pacific Time) 04/09/2015 07:00 am
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