Up A Level "And" "And" of An "Or" Contrapositive "For All" "If and Only If" "If..., Then..." "Not" "Not" of An "And" "Not" of An "If...Then" "Not" of An "Or" "Or" "Or" of An "And" Short Tautologies "There exists"
 
"OR" DISTRIBUTES OVER "AND"
Let P, Q, and R be sentences, each of which is true or false (and none of
which is both). The two truth tables below shows that "and" distributes
over "or". To be specific, "P or (Q and R)" means the same thing as
"(P or Q) and (P or R)". In the arithmetic of real numbers, this is
similar to the rule that a*(b+c)=(a*b)+(a*c).
"Or" Distributes Over "And", I
P  Q  R 
Q and R  P or (Q and R) 
T  T  T  T 
T 
T  T  F  F 
T 
T  F  T  F 
T 
T  F  F  F 
T 
F  T  T  T 
T 
F  T  F  F 
F 
F  F  T  F 
F 
F  F  F  F 
F 
"Or" Distributes Over "And", II
P  Q  R 
P or Q  P or R  (P or Q) and (P or R) 
T  T  T  T 
T  T 
T  T  F  T 
T  T 
T  F  T  T 
T  T 
T  F  F  T 
T  T 
F  T  T  T 
T  T 
F  T  F  T 
F  F 
F  F  T  F 
T  F 
F  F  F  F 
F  F 
