Thread: Truth Table for discrete math logic

mn

Hello, chillerbros17!

The exclusive-or operation is defined by the following truth table:

Code:

 p  q | p v q 
------+------- 
 T  T |   F 
 T  F |   T 
 F  T |   T
 F  F |   F

Exclusive-or means "p or q but not both".

a. Express p v q in terms of p, q, v, ^, ~

I would write: .(p ^ ~q) v (~p ^ q)

b. Express p v q in terms of p, q, ^, ~, v

Tricky . . . the "or" is not in the list.

So I can't write: .p v q

But I can use DeMorgan's Law to write: .~(~p ^ ~q)

. . (This works: It says "It is not true that both are false".)

c. Show that one of the distributive laws no longer holds when v is replaced by v.

Compare: . p v (q ^ r) .and ,(p v q) ^ (p v r)

Code:

 p v (q ^ r)      (p v Q) ^ (P v R)
------------      -----------------
 T F  T T T        T F T  F  T F T
 T T  T F F        T F T  F  T T F
 T T  F F T        T T F  F  T F T
 T T  F F F        T T F  T  T T F
 F T  T T T        F T T  T  F T T
 F F  T F F        F T T  F  F F F
 F F  F F T        F F F  F  F T T
 F F  F F F        F F F  F  F F F
   ↑      not equal       ↑