a)
I have to verify the following, using equivalences. Can anyone help me please:
a) [( p Þq) and ( p Þnot q)] º not p
b) [(p and q) Û p ] º [p Þ q]
c) not ( p Ûq) º (p Ûnot q)
d) [(p and q Þ r) and (p and not q) Þ not r)] º [p Þ (q Û r)]
Can anyone double check my working please? I need to know if I'm doing these things correctly.
Thanks
[ ( P Ù Q ) Û ] º ( P Þ Q )
[ ( P Ù Q ) Þ ) ] Ù [ P Þ ( P Ù Q ) ] If and only if
[ Ø(P Ù Q ) Ú P ] Ù [ ØP Ú ( P Ù Q ) ] Implication
[ ( ØP ÚØQ ) Ú P ] Ù [ ØP Ú ( P Ù Q ) ] De Morgans
[ ( ØP Ú P ) ÚØQ ] Ù [ ØP Ú ( P Ù Q ) ] Associativity
[ True ÚØQ ] Ù [ ØP Ú ( P Ù Q ) ] Law of Excluded Middle
[ ØP Ú ( P Ù Q ) ] Removal Of Constant
( ØP Ú P ) Ù ( ØP Ú Q ) Distributivity
ØP Ú Q Law of Excluded Middle
P Þ Q Implication