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---
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layout : noteshome
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- title : Crib Sheet
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+ title : Logic and Verification
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+ math : true
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---
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## Logic crib sheet
@@ -26,17 +27,15 @@ X is a tautology if and only if $$\empty \vDash X$$ , which we write as $$\vDash
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#### Generalised disjunction
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- - $$ [X_1, X_2, ..., X_n] = X_1 \vee X_2 \vee ... \vee X_n $$
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-
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- - $$ v([X_1, X_2, ..., X_n]) = T $$ if and only if $$ v(X_i) = T, \quad \exists V_i $$
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- - $$ v([]) = v(\bot) = F $$
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+ -   ; $$ [X_1, X_2, ..., X_n] = X_1 \vee X_2 \vee ... \vee X_n $$
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+ -   ; $$ v([X_1, X_2, ..., X_n]) = T $$ if and only if $$ v(X_i) = T, \quad \exists V_i $$
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+ -   ; $$ v([]) = v(\bot) = F $$
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#### Generalised conjunction
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- - $$ \langle X_1, X_2, ..., X_n \rangle = X_1 \wedge X_2 \wedge ... \wedge X_n $$
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-
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- - $$ v(\langle X_1, X_2, ..., X_n \rangle) = T $$ if and only if $$ v(X_i) = T, \quad \forall V_i $$
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- - $$ v(\langle \rangle) = v(\bot) = F $$
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+ -   ; $$ \langle X_1, X_2, ..., X_n \rangle = X_1 \wedge X_2 \wedge ... \wedge X_n $$
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+ -   ; $$ v(\langle X_1, X_2, ..., X_n \rangle) = T $$ if and only if $$ v(X_i) = T, \quad \forall V_i $$
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+ -   ; $$ v(\langle \rangle) = v(\bot) = F $$
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### Normal forms
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