I encountered these two types of arrows that my instructors have been drawing every time they start a new line, and sometimes they draw one and not the other. I know one stands for "this implies", which is "=" The other stands for "if and only if", which is "" However, what I am having trouble with is when I am doing a general math problem, how do I know if I am to use one in the line and not the other, or use both?

Question

I encountered these two types of arrows that my instructors have been drawing every time they start a new line, and sometimes they draw one and not the other.

I know one stands for "this implies", which is "=>"
The other stands for "if and only if", which is "<=>"

However, what I am having trouble with is when I am doing a general math problem, how do I know if I am to use one in the line and not the other, or use both?

akshay_budhkar · Answer

depends on what you are solving

mostly you will encounter the implies sign which is used to solve a question whose solution has a number of steps following in a correct sequence. 

the second one is used only if there is a condition in that step like say x=3 if and only if x+1=y or something like that

anonymous · Answer

"if and only if", or "iff" for short is a lot stronger than just a one directional arrow.  To prove that :$$p\iff q$$

You need to prove two things:$$p\Longrightarrow q$$and$$q\Longrightarrow p$$
Not every statement is an "iff" statement.  for example:$$x^2=1\iff x=1$$would be incorrect because it is true that:$$x=1\Longrightarrow x^2=1$$it is NOT true that:$$x^2=1\Longrightarrow x=1$$x could be -1 as well.