Logic Rules

Front 1

Modus Ponens (MP)

ROI

Back 1

If p then q

p

So q

Front 2

Modus Tollens (MT)

ROI

Back 2

if p then q

not q

So not p

Front 3

Disjunctive Syllogism (DS)

ROI

Back 3

p or q

not p

So q

Front 4

Hypothetical Syllogism (HS)

ROI

Back 4

if p then q

if q then r

if p then r

Front 5

Simplification (SIMP)

ROI

Back 5

p and q

So p

Front 6

Conjunction (CONJ)

ROI

Back 6

p

q

So p and q

Front 7

Addition (ADD)

ROI

Back 7

p

So p or q

Front 8

Constructive Dilemma (CD)

ROI

Back 8

if p then q

if r then s

p or r

So q or s

Front 9

Destructive Dilemma (DD)

ROI

Back 9

if p then q

if r then s

not q or not s

So not p or not r

Front 10

Conversion/Communitivity (COM)

ROE

Back 10

p or q = q or p

Or

p and q = q and p

Front 11

Double Negation (DN)

ROE

Back 11

p = not not p

Front 12

Contraposition/Transposition (CONTRA)

ROE

Back 12

if p then q = if not q then not p

Front 13

Material Equivalence (ME)

ROE

Back 13

p if-and-only-if q =

(if p then q) and (if q then p)

Or

p if-and-only-if q =

(p and q) or (not p and not q)

Front 14

Tautology (TAUT)

ROE

Back 14

p or p = p

Or

p and p = p

Front 15

Association (ASSOC)

ROE

Back 15

(p or q) or r =

p or (q or r)

Or

(p and q) and r =

p and (q and r)

Front 16

De Morgan's Law (DM)

ROE

Back 16

not (p or q) =

not p and not q

Or

not (p and q) =

not p or not q

Front 17

Distribution (DIST)

ROE

Back 17

p or (q and r) =

(p or q) and (p or r)

Or

p and (q or r) =

(p and q) or (p and r)

Front 18

Exportation (EXP)

ROE

Back 18

if (p and q) then r =

if p then (if q then r)

Front 19

Material Implication (IMP)

ROE

Back 19

if p then q = not p or q

Or

p or q = if not p then q