Laws of Proposition

[solomon_13000]

Show that ~(p \/ (~p /\ q)) = ~p /\ ~q by using the Laws of Proposition

my solution:

~(p \/ (~p /\ q))
~p /\ ~(~p /\ q)
~p /\ (p \/ ~q)
(~p /\ p) \/ (~p /\ ~q)
F /\ (~p /\ ~q)


Show that ~p /\ ~(p /\ q) = ~p using Laws of Proposition.

My solution:

~p /\ ~(p /\ q)
~p /\ (~p \/ ~q)
~p \/ (~p /\ ~q)


Is my steps correct?

 

[pka]

Show that ~(p \/ (~p /\ q)) = ~p /\ ~q by using the Laws of Proposition

my solution:

~(p \/ (~p /\ q))
~p /\ ~(~p /\ q)
~p /\ (p \/ ~q)
(~p /\ p) \/ (~p /\ ~q)
F \/ (~p /\ ~q) should be or.


Show that ~p /\ ~(p /\ q) = ~p using Laws of Proposition.

My solution:

~p /\ ~(p /\ q)
~p /\ (~p \/ ~q)
~p \/ (~p /\ ~q)
~p\/F
~p

Is my steps correct?

Otherwise correct.