ALGEBRA
POSITION
(Adrian R. Arevalo)
Prove that
¬(¬p∧¬q)∧¬(p∨q)≡ T∧F
• First use the De morgans law by distributing
the negation sign in the variable inside the
parenthesis next to it and change its operation
to make the equation like this.
• ¬(¬p∧¬q)∧¬(p∨q)≡ T∧F
• ￢￢p∨￢￢q∧￢p∧￢q≡ De Morgans Law
Prove that
¬(¬p∧¬q)
∧¬(p∨q)≡
T∧F
2nd Used the double negation law
to eliminate the double negations.
¬(¬p∧¬q) ∧¬(p∨q)≡ T∧F
￢￢p∨￢￢q∧￢p∧￢q≡ De
Morgans
p∨q∧￢p∧￢q
≡ Double negation
Prove that
¬(¬p∧¬q)∧¬(p∨q)≡ T∧F
• 3rd use the commutative law to arrange the equation or
the make the same variable next to each other.
• ¬(¬p∧¬q) ∧¬(p∨q)≡ T∧F
• ￢￢p∨￢￢q∧￢p∧￢q≡ De Morgans
• p∨q∧￢p∧￢q
≡ Double negation
• p∨￢p∧q∧￢q
≡ Commutative
Prove that
¬(¬p∧¬q)∧¬(p∨q)≡
T∧F
4th use the identity law to get its true
value.
¬(¬p∧¬q) ∧¬(p∨q)≡ T∧F
￢￢p∨￢￢q∧￢p∧￢q≡ De Morgans
P∨q∧￢p∧￢q
≡ Double negation
P∨￢p∧q∧￢q
≡ Commutative
T∧F
≡ Identity