- #1
MathematicalPhysicist
Gold Member
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i searched in the homework section and there isn't a section for logic an set theory so i ask my questions here (begging for replies):
1)expand the proposition (by the equivalence rules):
[~(pvq)v((~p)^q)]
i got to this: [(~pv~p)^(~pv~q)]^[(qv~p)^(qv~q)]
is it correct?
2) prove/disprove:
(Ex)(Ay)p(x,y)<=> (Ay)(Ex)p(x,y)
which means to prove that the double implication is tautology.
so i have assumed that:
T-(Ex)(Ay)p(x,y)
T-(Ay)p(a,y)
T-p(a,y)
T-(Ea)p(a,y)
T-(Ay)(Ex)P(x,y)
is this correct or where i am wrong?
your replies is much appreciated.
1)expand the proposition (by the equivalence rules):
[~(pvq)v((~p)^q)]
i got to this: [(~pv~p)^(~pv~q)]^[(qv~p)^(qv~q)]
is it correct?
2) prove/disprove:
(Ex)(Ay)p(x,y)<=> (Ay)(Ex)p(x,y)
which means to prove that the double implication is tautology.
so i have assumed that:
T-(Ex)(Ay)p(x,y)
T-(Ay)p(a,y)
T-p(a,y)
T-(Ea)p(a,y)
T-(Ay)(Ex)P(x,y)
is this correct or where i am wrong?
your replies is much appreciated.