Conjunction Introduction

& I

How to apply &I Forwards

  1. Select &I 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. Select the line on which the desired right-hand conjunct appears in the Fitch.
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  4. Click the Apply Rule button in the ToolBox.
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How to apply &I Backwards

  1. Select &I from the Intro Rules menu in the ToolBox.
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  2. Select the conjunction 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 &I, click on the statement below that best describes the problem you're having.

I can't select &I 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 formulae I want to conjoin 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 conjunction 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 &I backwards, I got an error message saying that the goal formula was not a conjunction.

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

If the formula is definitely a conjunction 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 either two lines in the Fitch or a conjunction in the Goal Tree. If your selections are correct, the instantiation pane of the ToolBox will be auto-filled with the left conjunct, right conjunct, and the conjunction, respectively.

If the rule instantiation 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 &I forwards to more or fewer than two lines.

Conjunction introduction is applied to two lines, or in rare cases, to the same line twice. As long as two selections have been made in the Fitch, the rule should produce a conjunction when derived, as there are no restrictions on the formulae to which the rule is applied.

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

You probably just selected the wrong lines, or selected the lines in the wrong order. Check the justification for the new line in the Fitch to verify whether this is the case.

Show me where to look for the justification

If the conjunction you wish to derive is present in the Goal Tree, you can always apply &I backwards to this conjunction in order to eliminate the possibility of making incorrect selections in the Fitch.

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