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Definition
| the conditional. only FALSE when T/F. |
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Definition
| the conjunction. ONLY TRUE when T/T. |
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Definition
| the disjunction. ONLY FALSE when F/F. |
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Definition
| the biconditional. ONLY TRUE when T/T or F/F. |
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Term
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Definition
| a negation. write the opposite sign of whatever is given. |
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Term
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Definition
| If a path in your tree contains a wff φ and also its negation ~ψ; close the path. |
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Term
| (~~) double negation rule |
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Definition
| If an open path contains an unchecked wff ~~φ, check it write φ at the bottom of each open path passing through the original wff ~~φ. |
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Term
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Definition
| If an open path contains an unchecked wff φ and ψ, check it and write first φ then ψ at the bottom of every open path passing through the original wff. NO BRANCHES. |
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Term
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Definition
| If an open path contains an unchecked wff φ v ψ, check it and split the bottom of each open path on which φ v ψ occurs into two branches, at the end at the right of which ψ. |
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Term
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Definition
| If an unchecked wff φ → ψ occurs on an open path, check it and then split the bottom of each open path on which this wff occurs into two, writing ~φ at the bottom of the left branch and ψ at the bottom of the right. |
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Term
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Definition
| If an unchecked wff ~(φ v ψ) occurs on an open path, check it and write first ~φ, then ψ at the bottom of each open path passing through the original wff. |
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Term
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Definition
| If an unchecked wff ~(φ → ψ) occurs on an open path, check it and write first φ, then ~ψ at the bottom of each open path passing through the original wff. |
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Term
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Definition
| If an unchecked wff ~(φ & ψ) occurs on an open path, check it and then split the bottom of each open path on which this wff occurs into two, writing ~φ at the bottom of the left branch and ~ψ at the bottom of the right. |
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