Logic

- anonymous

Logic

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- anonymous

|dw:1348907509327:dw|

- anonymous

if 'a', then 'b' : a-> b

- anonymous

is that correct ?.. can i write teh same as,
only if 'b', then 'a' ?

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## More answers

- anonymous

Are you asking if you can reverse "if A, then B" to "if B, then A"?

- anonymous

no, the thing troubling me is "only if"

- anonymous

That doesn't sound right. "Only if" B still has many things that aren't A.

- anonymous

actually i dont get "if and only if", im trying to understand it by breaking it down to "if" and "only if"

- anonymous

may i knw why it doesnt sound right to you, it does sound right to me

- anonymous

But... a square is a kind of a rectangle.

- anonymous

|dw:1348907860375:dw|

- anonymous

"A square cannot be a rectangle"?

- anonymous

excuse me, my question is different, plz look at the diagram what im asking

- anonymous

only if its b, then only it can be a

- UnkleRhaukus

##### 1 Attachment

- anonymous

"In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles."
"In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles (90-degree angles, or right angles)."
So a square shares all the properties of a rectangle, but has the additional condition that it's regular. So all squares are rectangles.

- anonymous

a doesnt have any possibility outside b

- anonymous

No, but just because it's B doesn't necessarily mean it's A.

- anonymous

Replace A with "it rained last night" and B with "the grass was wet the next morning".

- anonymous

There are many ways for the grass to be wet the next morning (dew, sprinklers), even if it raining last night necessarily means that the grass is wet next morning.

- anonymous

@UnkleRhaukus you got me correctly! 3rd point in ur snapshot says it

- anonymous

Ahh, okay, the third point. I thought you were saying something else. My bad.

- anonymous

its okay... i dont get "if and only if" could you walk me through slowly plz

- anonymous

ive understood "only if" i guess, whats "if and only if",
i mean i knw it means,
a iff b
is same as
a->b, b->a

- anonymous

but why it is called "if and only if" is confuses me

- UnkleRhaukus

\[\begin{array}{ccccc}\phi&\psi&\phi\Rightarrow\psi&\phi \Leftarrow\psi&\phi\Leftrightarrow\psi\\ \hline \\T&T&T&T&T\\T&F&F&T&F\\F&T&T&F&F\\F&F&T&T&T\end{array}\]

- anonymous

Unkle, is it just me, or is "only if B then A" different from "A iff B"?

- anonymous

only if B then A is different from A if and only if B.

- anonymous

im familiar with xnor truth table, but still why its called "if and only if"
should we break it into two : 1) if, 2) only if

- anonymous

a iff b
break as :
if a then b,
a only if b
?

- zzr0ck3r

@sara12345 do you understand if a then b?

- UnkleRhaukus

if and only if \(\Leftrightarrow\) iff

- anonymous

yes, i understood iff also, only the "phrase" is confusing me

- zzr0ck3r

I think I'm confused about what your asking. Sorry.

- anonymous

sorry, like
a iff b
can i break it into 2 pieces :
1) if a then b,
2) a only if b ?

- anonymous

the two broken statements, do they cover completely "a iff b" ?

- anonymous

il start over.

- UnkleRhaukus

these statements say the same thing
1) if a then b,
2) a only if b
_______

- anonymous

ohh yea they say same thing, a->b

- UnkleRhaukus

to meant the same as a iff b
switch the letters around in one of them

- anonymous

so hw can iu break it meanigfully

- anonymous

a "if and only if " b : a <--> b
a "if" b : b->a
a "only if" b : a->b
i guess now i have it working in above

- anonymous

i see there is lot of difference between,
"if" and "only if"

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