Hi

I am little confused about the following statements.

$\displaystyle 1) \;\left[\exists x P(x)\right]\Rightarrow M(x)$

and

$\displaystyle 2) \forall x \left[P(x)\Rightarrow M(x)\right]$

Its obvious that they are not logically equivalent. But lets take some examples.

let P(x) = x is majoring in maths

M(x)= x is mad.

so the statement 2 means thatall math majors are madand

statement 1 means thatif there is a math major then he is mad

here it looks like they are equivalent in meaning. so whats happening ?