Disjunction Introduction

vIL
vIR

How to apply vIL Forwards

  1. Select vIL from the Intro Rules menu in the ToolBox.
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  2. Select the line on which the desired right-hand conjunct appears in the Fitch.
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  3. Click in the text area of the instantiation pane in the ToolBox, and enter the desired left-hand conjunct using the keyboard.
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  4. Click the Apply Rule button in the ToolBox.
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How to apply vIR Forwards

  1. Select vIR from the Intro Rules menu in the ToolBox.
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  2. Select the line on which the desired left-hand conjunct appears in the Fitch.
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  3. Click in the text area of the instantiation pane in the ToolBox, and enter the desired right-hand conjunct using the keyboard.
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  4. Click the Apply Rule button in the ToolBox.
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How to apply vIL Backwards

  1. Select vIL from the Intro Rules menu in the ToolBox.
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  2. Select the disjunction you want to derive in the Goal Tree.
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  3. Click the Apply Rule button in the ToolBox.
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How to apply vIR Backwards

  1. Select vIR from the Intro Rules menu in the ToolBox.
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  2. Select the disjunction you want to derive in the Goal Tree.
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  3. Click the Apply Rule button in the ToolBox.
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Troubleshooting

If you're having trouble applying either vIL or vIR, click on the statement below that best describes the problem you're having.

I can't select vIL/vIR from the Intro 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 formula I want as a dijsunct 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 formulae no matter where you click on them, try exiting the CPL and reloading the problem. If the problem persists after reloading, please inform your instructor.

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I can't select the disjunction I want to derive in the Goal Tree.

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 when attempting to apply vIL/vIR backwards, I got an error message saying that the goal formula was not a disjunction.

Disjunction introduction can only be used to derive disjunctions. Check carefully to make certain that the formula you are selecting in the Goal Tree really is a disjunction. Any disjunction will appear in the Goal Tree in the form ( φ v ψ ).

If the formula is definitely a disjunction 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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I'm having trouble entering the new disjunct in the input dialogue box.

The most likely source of trouble is an incorrectly entered connective. Here are the correct symbols and keystrokes (on standard U.S. keyboards) for each connective and operator:

OperatorSymbolKeystrokes
Conjunction&shift-7
Disjunctionv.v.
Conditional->- shift-.
Negation~shift-`
Biconditional<->shift-, - shift-.
Universal QuantifierA.A.
Existential QuantifierE.E.


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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, that you have selected a line in the Fitch or a disjunction in the Goal Tree, and if applying the rule forwards, that you have entered a formula in the instantiation pane of the ToolBox.

If these steps have been completed correctly, 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 vIL/vIR forwards to more than one line.

Disjunction introduction is applied to a single line. The formula on this line will be the right-hand conjunct of the formula derived when applying vIL, and it will be the left-hand disjunct when applying vIR.

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

You probably just selected the wrong line, or entered the wrong formula in the input dialogue. Check the justification for the new line in the Fitch and carefully inspect the added disjunct to verify whether this is the case.

Show me where to look for the justification

If the disjunction you wish to derive is present in the Goal Tree, you can always apply vIL/vIR backwards to this disjunction in order to eliminate the possibility of making incorrect selections in the Fitch.

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