- #1

- 912

- 19

I am little confused about the following statements.

[tex]1) \;\left[\exists x P(x)\right]\Rightarrow M(x)[/tex]

and

[tex]2) \forall x \left[P(x)\Rightarrow M(x)\right][/tex]

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 that

**all math majors are mad**and

statement 1 means that

**if there is a math major then he is mad**

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