# Logic

##### Full Member
The statement is "IF you are the parent of two "yellow" children THEN you are a ZOMBIE". That says NOTHING about what happens if you are NOT "the parent of two yellow children".
but lemme ask you before that, The statement is "IF you are the parent of two "yellow" children THEN you are a ZOMBIE". that says nothing about what happens if just one of its children yellow? I mean can I conclude from "IF you are the parent of two "yellow" children THEN you are a ZOMBIE" that his children must be "Yellow" ?

#### Otis

##### Elite Member
... if the parent doesn't have children then ...
If a person has no children, they are not a parent.

#### HallsofIvy

##### Elite Member
"but lemme ask you before that, The statement is "IF you are the parent of two "yellow" children THEN you are a ZOMBIE". that says nothing about what happens if just one of its children yellow? I mean can I conclude from "IF you are the parent of two "yellow" children THEN you are a ZOMBIE" that his children must be "Yellow" ?"
That whose children must be "yellow"? The statement "if p then q" tells you what happens if p is true. it says nothing about what happens if p is not true.

Now you have another question: 'can I conclude from "IF you are the parent of two "yellow" children THEN you are a ZOMBIE" that his children must be "Yellow"'. Certainly if the hypothesis, "IF you are the parent of two "yellow" children" is true then his children must be "yellow"! That's obvious!

##### Full Member
x,y is variables, "=" is equal like math "=" ..nothing else.
what's struggling me is: yeah x=y right? but who will ensure for me that if I progress in my analysis and arrived to y=z, that's x=y still right? if so then we can say x=z ! but if I didn't change the equation x=y who ensure for me that it's really didn't change that equation and still right for any circumstances ?!

what's confusing me this:
(1) x=y ..so fine with that.
after 5minutes of thinking and analysing problem, I get
(2) y=z

then we conclude that x=z, but what's confusing me why it's that right? who ensures that the first equation is still right and none changed it?! that's what confusing me alot!!!

##### Full Member
When we say $$\displaystyle x = y$$,

we mean that x and y represent the same thing. They are just different names for the same thing. If you own only one dog and it is named Toto, it makes no difference whether you say "my dog" or "Toto" because both refer to the same animal.

By "same thing" in math, we frequently mean "have the same numerical value."

So I can say $$\displaystyle 13 + 3 = 21 - 5$$

because both expressions evaluate to the same result, namely 16.

You seem to be taking something that is easy and making it hard. In the case of 13 + 3 and 21 - 5, the expressions themselves are different, but the value of the expressions is identical. We look beyond the superficial form of the expressions and consider the quantitative meaning represented by the expressions.

So yes we can replace 13 + 3 by 21 - 5 or replace 21 - 5 by 13 + 3 because both expressions are quantitatively identical.
I got you !
but lemme ask something else, if I assign "my dog"=z , then we can call "my dog" as z?! what's confusing me, we must define "my dog" =: z and not "my dog" = z ! there's difference between "=" and "=:"(definition in math) .. but it seems the same ? I mean the mean of "=" is the same as "=:" ?!

##### Full Member
Are you talking about equality vs assignment?
well what's confusing me is how can I do x=y and then say that's y is the same as x, but I didn't before define what's y !

#### lev888

##### Senior Member
Could you post an example of a problem that involves the issue that's confusing you? Otherwise it's very hard to understand you.

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