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19 Cards in this Set
 Front
 Back
X → Y X —————— Y 
Modus ponens (MP) If X → Y and X are both lines in your proof, you can add a new line with the statement Y. This lineis justified by citing the modus ponens rule, MP, and the lines containing X → Y and X. 

X → Y ~Y —————— ~X 
Modus tollens (MT) If X → Y and ~Y are both lines in your proof, you can add a new line with the statement ~X. Thisline is justified by citing the modus tollens rule, MT, and the lines containing X → Y and ~Y. 

X ∨ Y ~X —————— Y or X∨Y ~Y —————— X 
Disjunctive syllogism (DS) If X ∨ Y and ~Y are both lines in your proof, you can add a new line with the statement X. This lineis justified by citing the disjunctive syllogism rule, DS, and the lines containing X ∨ Y and ~Y. 

X & Y —————— Y or X & Y —————— X 
Simplification (SIMP) If X & Y is a line in your proof, you can add a new line with the statement X or a new line with thestatement Y. This new line is justified by citing the simplification rule, SIMP, and the line containingX & Y. 

X → Y Y → Z —————— X→Z 
Hypothetical syllogism (HS) If X → Y and Y → Z are both lines in your proof, you can add a new line with the statement X → Z.This line is justified by citing the hypothetical syllogism rule, HS, and the lines containing X → Y andY → Z. 

X —————— X ∨ Y 
Addition (ADD) If X is a line in your proof, you can add a new line with the statement X ∨ Y. This line is justified byciting the addition rule, ADD, and the line containing the statement X. 

X Y —————— X&Y or Y&X 
Conjunction (CONJ) If X and Y are both lines in your proof, you can add a new line with the statement X & Y or a newline with the statement Y & X. This line is justified by citing the conjunction rule, CONJ, and thelines containing X and Y. 

X∨Y —————— Y∨X or X&Y —————— Y&X 
The Commutation Rule(COMM) If X ∨ Y is a line in your proof, you can add a new line with the statement Y ∨ X. If X & Y is a line in your proof, you can add a new line with the statement Y & X. Justify this new line by citing (by number) the line used and the rule, COMM. 

W → X Y → Z W ∨ Y —————— X∨Z 
Constructive dilemma (CD) If W → X, Y → Z, and W ∨ Y are all lines in your proof, you can add a new line with the statementX ∨ Z. This line is justified by citing the constructive dilemma rule, CD, and the lines containing W→ X, Y → Z, and W ∨ Y. 

~~X —————— X 
The Double Negation Rule (DN) If X is a line in your proof, you can add a new line with the statement ~~X, and vice versa: If ~~X isa line in your proof, you can add a new line with the statement X. Justify this new line by citing (by number) the line used and the rule, DN. 

(X ∨ Y) ∨ Z —————— X ∨ (Y ∨ Z) or (X & Y) & Z —————— X & (Y & Z) 
The Association Rule(ASSOC) If (X ∨ Y) ∨ Z is a line in your proof, you can add a new line with the statement X ∨ (Y ∨ Z), andvice versa; If X ∨ (Y ∨ Z) is a line in your proof, you can add a new line with the statement (X ∨ Y)∨ Z. If (X & Y) & Z is a line in your proof, you can add a new line with the statement X & (Y & Z), andvice versa; If X & (Y & Z) is a line in your proof, you can add a new line with the statement (X & Y)& Z. Justify this new line by citing (by number) the line used and the rule, ASSOC. 

X ∨ (Y & Z) —————— (X ∨ Y) & (X ∨ Z) or X & (Y ∨ Z) —————— (X & Y) ∨ (X & Z) 
The Distribution Rule(DIST) If X ∨ (Y & Z) is a line in your proof, you can add a new line with the statement (X ∨ Y) & (X ∨Z), and vice versa; If (X ∨ Y) & (X ∨ Z) is a line in your proof, you can add a new line with thestatement X ∨ (Y & Z). If X & (Y ∨ Z) is a line in your proof, you can add a new line with the statement (X & Y) ∨ (X &Z), and vice versa; If (X & Y) ∨ (X & Z) is a line in your proof, you can add a new line with thestatement X & (Y ∨ Z). Justify this new line by citing (by number) the line used and the rule, DIST. 

X → Y —————— ~Y → ~X 
The Transposition Rule(TRANS) If X → Y is a line in your proof, you can add a new line with the statement ~Y → ~X, and viceversa: If ~Y → ~X is a line in your proof, you can add a new line with the statement X → Y. Justify this new line by citing (by number) the line used and the rule, TRANS. 

X → Y —————— ~X ∨ Y 
The Implication Rule (IMP) If X → Y is a line in your proof, you can add a new line with the statement ~X ∨ Y, and vice versa:If ~X ∨ Y is a line in your proof, you can add a new line with the statement X → Y. Justify this new line by citing (by number) the line used and the rule, IMP. 

X↔Y —————— (X → Y) & (Y →X) 
The Equivalence Rule (EQUIV) If X ↔ Y is a line in your proof, you can add a new line with the statement (X → Y) & (Y → X),and vice versa: If (X → Y) & (Y → X) is a line in your proof, you can add a new line with thestatement X ↔ Y. Justify this new line by citing (by number) the line used and the rule, EQUIV. 

(X & Y) → Z —————— X → (Y → Z) 
The Exportation Rule (EXP) If (X & Y) → Z is a line in your proof, you can add a new line with the statement X → (Y → Z), andvice versa: If X → (Y → Z) is a line in your proof, you can add a new line with the statement (X &Y) → Z. Justify this new line by citing (by number) the line used and the rule, EXP. 

~(X & Y) —————— ~X ∨ ~Y or ~(X ∨ Y) —————— ~X & ~Y 
DeMorgan's Law (DM) If ~(X & Y) is a line in your proof, you can add a new line with the statement ~X ∨ ~Y, and viceversa: If ~X ∨ ~Y is a line in your proof, you can add a new line with the statement ~(X & Y). If ~(X ∨ Y) is a line in your proof, you can add a new line with the statement ~X & ~Y, and viceversa: If ~X & ~Y is a line in your proof, you can add a new line with the statement ~(X ∨ Y). Justify this new line by citing (by number) the line used and the rule, DM. 

~X Z & ~Z —————— X 
Indirect Proof (IP) If from the assumption ~X (and possibly other assumptions), you can prove a contradiction, i.e. anystatement of the form Z & ~Z, then you can add a new line X. Justify this new line by citing theindirect proof rule (IP) and all the lines in your subproof. 

X Y —————— X → Y 
Conditional Proof (CP) If, from the assumption X (and possibly other assumptions), you can prove Y, then you can add anew line X → Y. This line is justified by citing the conditional proof rule, CP, and all the lines used inyour subproof. 