Interval Notation: difference between 'and' and 'or'

[Guest]

I was curious when you are writing something in interval notation what the difference is between AND and OR, example:

x ≤ -3 AND x > -10

x > 2 OR 5 < x

I just started to understand interval notation but that threw me off and I couldnt find anything in the text about the difference. I am new on this board, so if you would be so kind, please post something about the difference.

THANK YOU.

 

[stapel]

"And" means a given x-value has to satisfy both statements.

"Or" means a given x-value has to satisfy at least one statement.

I would suspect that the second compound inequality was actually "x < 2 or x > 5", as "x > 2 or x > 5" just means "x > 2" (since anything greater than 5 is necessarily greater than 2). If my surmise is correct, then qualifying x-values would be less than 2 or else more than 5, but not anything between 2 and 5. That is, the x-values would satisfy |x - 3.5| > 1.5.

The first compound inequality just says that the x-value have to be less than or equal to -3 and also greater than -10; that is, they have to lie within the interval (-10, -3]. If this had been an "or" inequality, then any x-value would have been fine, since any x-value would be less than -3 (which includes -10 and everything before it), greater than -10 (which includes -3 and everything after it), or else between the two numbers.

Eliz.