Disjunction Elimination

vE

How to apply vE

  1. Select vE from the Elim Rules menu in the ToolBox.
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  2. Select the disjunction to be eliminated in the Fitch.
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  3. Select the last line of the subderivation opened by the assumption of the left-hand disjunct in the Fitch. The formula on this line should be the formula you want to derive.
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  4. Select the last line of the subderivation opened by the assumption of the right-hand disjunct in the Fitch. The formula on this line should be the formula you want to derive.
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  5. Click the Apply Rule button in the Toolbox.
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Troubleshooting

If you're having trouble applying vE, click on the statement below that best describes the problem you're having.

I can't select vE from the Elim Rules menu.

If a rule is not appearing in the ToolBox menus, then that rule is not available for the currently loaded problem. Rules are available only for derivation problems that follow the presentation of the rule in the text, regardless of what problems you may have completed previously.

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I can't select the disjunction or the final lines of the two subderivations in the Fitch.

First, make sure that there isn't a problem with your mouse by clicking to change applications or browser windows. If your mouse is working properly, try clicking on different parts of the formula. If you are still unable to select the formula no matter where you click on it, try exiting the CPL and reloading the problem. If the problem persists after reloading, please inform your instructor.

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When I clicked the Apply Rule button, I got an error message that said the formulae I had selected were not of the correct form.

If you have selected the disjunction to be eliminated, and the final lines of the two subderivations opened with the assumptions of the left and right disjuncts, in that order, but you still get the same error message when applying the rule, try exiting the CPL and then reloading the problem. If the problem persists after reloading, please inform your instructor.

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When I clicked the Apply Rule button, I got another error message or nothing happens.

Make sure that you have selected the correct rule in the ToolBox, and that you have selected disjunction to be eliminated, and the final lines of the two subderivations opened with the assumptions of the left and right disjuncts (in that order) in the Fitch. If your selections are correct, the formula that will be derived when the rule is applied will auto-fill in the instantiation pane of the ToolBox.

If the formula is auto-filled, but you continue to experience problems when attempting to apply the rule, try exiting the CPL and reloading the problem. If the problems persist after reloading, please inform your instructor.

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I'm trying to apply vE backwards.

Elimination rules can't be applied backwards in the CPL.

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I'm trying to apply vE to more or fewer than three lines.

vE is applied to three lines. The first line is that on which the disjunction to be eliminated appears. The second line is the final line of the subderivation opened with the assumption of the left-hand disjunct, and the third line is the final line of the subderivation opened by the assumption of the right-hand disjunct. Also recall that the formale on the last lines of the two subderivations must be identical in order for the rule application to be valid.

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I can apply the rule successfully, but the wrong formula is derived.

Check the justification for the new line in the Fitch to make sure you applied the rule in the way you expected. The formula derived will be the same as that on the last line of each subderivation.

Show me where to look for the justification

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