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I am trying to figure this out but have no clue where to even begin. Yes this is a question from a logic homework I have but I do not want an answer, just want to know how to approach this. I know all the logic concepts (demorgans law, dis-junction, conjunction, CDF formulas, etc...). I just don't know how to apply them here. Any ideas ? Here is the question.

“Bob has money. The car is silver. The car is fast. If the car is silver or if the car is fast, and Bob has money then Bob goes on vacation on a cruise.”

Formalize and prove or disprove this claim: Bob goes on vacation on a cruise.

Justify your answer using the resolution by refutation method.

I made this equation after reading some of the comments and answers:

A = Bob has money

B = The car is silver

F = The car is fast

C = Bob goes on vacation on a cruise

(B ∨ F) ∧ A → C

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  • $\begingroup$ "Bob has money" is $p$. "The car is silver" is $q$ and "The car is fast" is $r$. $\endgroup$ – Mauro ALLEGRANZA Feb 19 '17 at 19:57
  • $\begingroup$ "Bob goes on vacation on a cruise” is $s$. $\endgroup$ – Mauro ALLEGRANZA Feb 19 '17 at 19:58
  • $\begingroup$ Then you have to formalize "If the car is silver or if the car is fast, and Bob has money then Bob goes on vacation on a cruise” using the logical connectives : $\lor$ for or, $\land$ for and and $\to$ for "if..., then___". $\endgroup$ – Mauro ALLEGRANZA Feb 19 '17 at 19:58
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Start off by assigning a symbol to each of your four propositions("Bob has money" may be represented by $B$, "car is silve"r by $S$ and so on..). Then convert the statement "the car is silver or if the car is fast, and Bob has money" into formal notation using conjunction/disjunction appropriately. In the last part, you say that the truth of the previous statement, implies that $V$ is true, where $V$ represents the proposition "Bob goes on vacation on cruise.".

Show your work, so that we can point out stuff if necessary and use notation consistently.

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  • $\begingroup$ Is the equation I came about correct ? $\endgroup$ – CodeDexter Feb 19 '17 at 20:29
  • $\begingroup$ Yes, it is. To conclude that the implication is true simply show that the left-hand side is true. Although as you progress, that's something you can leave out as obvious(subject to your instructor's opinion). Another thing you might want to do is read up on conditionals and vacuous truth. $\endgroup$ – Akay Feb 19 '17 at 21:47
  • $\begingroup$ To be clear, I meant leave it out only when the predicates are few and simple. As in this case - all are true. $\endgroup$ – Akay Feb 20 '17 at 5:39

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