Question

What is the difference between AND and OR..... @satellite73 can u PLZ explain. I always get confused there

Answer 1

and means both are true

Answer 2

so when you write \(x<0\) and \(x>2\) there is no such number, because no number is less than zero and at the same time greater than 2

Answer 3

u can use and when your saying I want apples and oranges
u use or when ur mentioning only one thing like u r saying would you like to have oranges or apples :P I think that is :P

Answer 4

Oh ya

Answer 5

The words "and" and "or" can be ambiguous in English, so in math we
give them precise meanings. We have to teach those meanings, but
often forget to, which may have happened here.

When we talk about the set of things that are A AND B, we mean that
EACH of those things must be BOTH A and B. Nothing is both a spoon
and a fork! (At least not in this problem.) So "and" would have been
inappropriate. There are no utensils that are spoons and forks.

When we talk about the set of things that are A OR B, we mean that
EACH of them may be EITHER A or B. That is, we are including in the
set BOTH those that are A, AND those that are B. This is where the
confusion and ambiguity come in! There are 8 utensils that are
spoons or forks.

Your son read it in a way that is commonly used in nontechnical
English, taking "How many are A or B" to mean two separate questions
combined: "How many are A, how many are B". I can see how that could
be tempting in this case; the two numbers happen to be the same, so
he could take the question to mean "How many are A (which is also
the same as the number that are B". If there had been 3 spoons and 4
forks, that interpretation would not have made as much sense; the best
answer he could give would be "3, or 4". We don't combine questions
like that in math, to avoid confusion.

So the book was right, but the question is ambiguous if the teacher
has not taught (or does not know) the standard mathematical usage.
(This usage is important in some later topics, such as probability,
so it's definitely worth teaching.)

Answer 6

if you have two separate intervals, for example, as a solution to an inequality, it is an "or" statement
x is less that 0 or x is greater than 2

Answer 7

it is the difference between \(A\cup B\) and \(A\cap B\)
first one is "or" second one is "and"

Answer 8

a<x<b means x is greater than a and less than b

Answer 9

x^2-2x>=0
x^2-2*x*1+1^2>=1^2
(x-1)^2>=1 (x-1)^2>=(+-1)^2
Now,
x-1<=-1 AND x-1>=1
x<=0 AND x>=2

Answer 10

So there should have been OR instead of AND

Answer 11

Once you use ±, it becomes a plus OR minus statement

Answer 12

to be honest i cannot make heads nor tails of that method of solving
it is solved via \(x(x-2)\geq 0\)

Answer 13

So that method cannot be used

Answer 14

i am not saying that, i am saying i don't understand what it means
if i was going to solve \((x-1)^2\geq 1\) the first thing i would do is rewrite as\[x(x-2)\geq 0\] and solve that

Answer 15

He added 1 to both sides. It's not incorrect, just not the usual way to solve

Answer 16

especially when the problem started as \(x^2-2x\geq 0\) this method seems like going around the mulberry bush to get your answer