Representing the statement using Quantifiers I want to represent the statement "Some numbers are not real " using quantifiers. I have been told by my teacher that the correct way to represent this is
num(x)  : x is a number
real(x) : x is real

∃x (num(x) ^ ¬real(x)) 

This made sense, i can translate this statement into "There exist some x such that x is a number and x is not real.
But the answer i came up by myself is this one

∃x (num(x)=> ¬real(x))

In translation , There exist some x such that if x is a number then x is not real. 
I just can't get around why my answer is wrong, for some x ; if x is a number then x is not real. Doesn't that sound very similar to the statement "Some numbers are not real".
In one of the video lectures i saw  this  example which made me even more confused. 
"No dog is intelligent" 
dog(x) : x is a dog
intel(x) : x is intelligent
The representation was 

∀x (dog(x) ==> ¬intel(x))

if this representation is true, how is my representation of "Some numbers are not real" wrong. 
PS : I am just a beginner at Discrete math finding my way, please pardon me if the question doesn't meet the quality standards of the community. 

Your version is wrong because "A and B" is not the same as "if A, then B".
For instance, there exists a horse H such that if H is 50 feet tall, then I win the lottery.
It is sadly not true that there exists a horse H such that H is 50 feet tall and I win the lottery.
More pointedly, (A implies B) is true when A is false. Therefore, "there exists X such that if X is a number, then X is not real" is true when X, for instance, is a banana.
