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I'm currently in Symbolic Logic with homework assignments (not asking for people to do my homework for me) with questions such as the following:

(derive the conclusion using the eighteen rules of inference)

  1. R ⊃ B
  2. R ⊃ (B ⊃ F )
  3. B ⊃ (F ⊃ H )
    Conclusion: R ⊃ H

Two questions: is there a way to go through the logic, with the rules (if there are built-in symbolic logic rules), to arrive at the specific conclusion (there are always multiple ways to solve it, however)? And more importantly, how do I do symbolic logic in mathematica? I can't find any resources that mention how to do it with the relevance of the kind of symbolic logic I'm doing in my class.

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  • $\begingroup$ The superset, ⊃, stands for 'implication' in my class. $\endgroup$ – Paul Lemus May 18 '16 at 5:07
  • $\begingroup$ 1. Implies[R,B] 2. Implies[R,Implies[B,F]] 3. Division is not a logical operation. $\endgroup$ – Romke Bontekoe May 18 '16 at 5:51
  • $\begingroup$ Oh, that's the conclusion after the forward slash $\endgroup$ – Paul Lemus May 18 '16 at 6:02
  • $\begingroup$ Fixed @RomkeBontekoe $\endgroup$ – Paul Lemus May 18 '16 at 6:03
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I am no expert on Boolean logic, but this may be some start for you:

homework = Implies[r, b] && Implies[r, Implies[b, f]] && Implies[b, Implies[f, h]]
BooleanConvert[homework]
LogicalExpand[homework]
BooleanTable[homework, {r, b, f, h}]

You could check the documentation and the examples of these functions.

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