- #1
jamesd
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Homework Statement
C = (Ax)(EY) (p(X) -> p(Y))
D = (EX)(Ay) (p(X) -> p(Y))
Are C and D equivalent?
Homework Equations
Truth table for implication
T T -> T
T F -> F
F T -> T
F F -> T
The Attempt at a Solution
Well I believe C is true is all cases and is a tautology whilst D is not true.
C is true as you can set y = x to make p(Y) true if P(X) is true if x and y belong to the same set.
D is false for example if have p{n | n is prime}, and have x is 3 then p(X) will be true but for all y if x and y belong to N then some p(Y) will be false making the formula overall false.
Is this correct? Has anyone got any tips on whether this is right?