- #1

MathematicalPhysicist

Gold Member

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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.