Truth table for discrete math

[chillerbros17]

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

p q p V q
--------------------
T T F
T F T
F T T
F F F

a. express p V q in terms of p,q, v, ^, ~


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

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

Many text denote the exclusive or as \(\displaystyle p\underline \vee q\).

Now for part (a):
\(\displaystyle p\underline \vee q \equiv \left( {p \wedge \sim q} \right) \vee \left( { \sim p \wedge q} \right)\).

Part (b):
\(\displaystyle p \vee q \equiv \sim \left( { \sim p \wedge \sim q} \right)\).