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

 Go to an overview of logic. Go to the home page for Tom Ramsey Go to the home page for the UHM Department of Mathematics Your comments and questions are welcome. Please email them ramsey@math.hawaii.edu.