SOLUTION: Prove this 1. F∨~I 2. I∨H 3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F

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Question 1208642: Prove this
1. F∨~I
2. I∨H
3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Here is one way to do the derivation. There may be other approaches.
NumberStatementLine(s) UsedReason
1F v ~I
2I v H
3~(G <--> J) --> ~H
:.[ (~G v ~J) & (G v J) ] --> F
4~F --> ~I1Material Implication
5~I --> H2Material Implication
6~F --> H4,5Hypothetical Syllogism
7~H --> F6Transposition
8~(G <--> J) --> F3,7Hypothetical Syllogism
9[ (~G v ~J) & (G v J) ] --> F8Material Equivalence

Here's a list of rules of inference and replacement