# Thread: Don't understand the and or thing

1. ## Don't understand the and or thing

Hi, I would like to know the reason why

( x <= n) ^ (x < n) ) is equivalent to (x <= n)

Because I think if n = 7

then first one can have value up to x = 7

but x < n can only have value up to x = 6

so since it is narrow the commonalities can exist up to x = 6...

so I thought it was (x < n) but the answer says ( x <= n ) let me know..

2. ## Re: Don't understand the and or thing

You are right. (x <= n) /\ (x < n) is equivalent to (x < n), not (x <= n).

3. ## Re: Don't understand the and or thing

Originally Posted by sekaiyoma
Hi, I would like to know the reason why
( x <= n) ^ (x < n) ) is equivalent to (x <= n)
What is the meaning of ( x <= n) ^ (x < n)?.

If it is set notation $(-\infty,n)\cap(-\infty,n]=(-\infty,n)$ then they not equivalent.
So what does it mean?

4. ## Re: Don't understand the and or thing

as always, emakarov's interpretation is correct. ^ stands for AND (logic) Thanks emakarov! the answer is wrong!