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 ↑