anonymous
  • anonymous
Logic
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1348907509327:dw|
anonymous
  • anonymous
if 'a', then 'b' : a-> b
anonymous
  • anonymous
is that correct ?.. can i write teh same as, only if 'b', then 'a' ?

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anonymous
  • anonymous
Are you asking if you can reverse "if A, then B" to "if B, then A"?
anonymous
  • anonymous
no, the thing troubling me is "only if"
anonymous
  • anonymous
That doesn't sound right. "Only if" B still has many things that aren't A.
anonymous
  • anonymous
actually i dont get "if and only if", im trying to understand it by breaking it down to "if" and "only if"
anonymous
  • anonymous
may i knw why it doesnt sound right to you, it does sound right to me
anonymous
  • anonymous
But... a square is a kind of a rectangle.
anonymous
  • anonymous
|dw:1348907860375:dw|
anonymous
  • anonymous
"A square cannot be a rectangle"?
anonymous
  • anonymous
excuse me, my question is different, plz look at the diagram what im asking
anonymous
  • anonymous
only if its b, then only it can be a
UnkleRhaukus
  • UnkleRhaukus
1 Attachment
anonymous
  • 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
  • anonymous
a doesnt have any possibility outside b
anonymous
  • anonymous
No, but just because it's B doesn't necessarily mean it's A.
anonymous
  • anonymous
Replace A with "it rained last night" and B with "the grass was wet the next morning".
anonymous
  • 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
  • anonymous
@UnkleRhaukus you got me correctly! 3rd point in ur snapshot says it
anonymous
  • anonymous
Ahh, okay, the third point. I thought you were saying something else. My bad.
anonymous
  • anonymous
its okay... i dont get "if and only if" could you walk me through slowly plz
anonymous
  • 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
  • anonymous
but why it is called "if and only if" is confuses me
UnkleRhaukus
  • 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
  • anonymous
Unkle, is it just me, or is "only if B then A" different from "A iff B"?
anonymous
  • anonymous
only if B then A is different from A if and only if B.
anonymous
  • 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
  • anonymous
a iff b break as : if a then b, a only if b ?
zzr0ck3r
  • zzr0ck3r
@sara12345 do you understand if a then b?
UnkleRhaukus
  • UnkleRhaukus
if and only if \(\Leftrightarrow\) iff
anonymous
  • anonymous
yes, i understood iff also, only the "phrase" is confusing me
zzr0ck3r
  • zzr0ck3r
I think I'm confused about what your asking. Sorry.
anonymous
  • anonymous
sorry, like a iff b can i break it into 2 pieces : 1) if a then b, 2) a only if b ?
anonymous
  • anonymous
the two broken statements, do they cover completely "a iff b" ?
anonymous
  • anonymous
il start over.
UnkleRhaukus
  • UnkleRhaukus
these statements say the same thing 1) if a then b, 2) a only if b _______
anonymous
  • anonymous
ohh yea they say same thing, a->b
UnkleRhaukus
  • UnkleRhaukus
to meant the same as a iff b switch the letters around in one of them
anonymous
  • anonymous
so hw can iu break it meanigfully
anonymous
  • 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
  • anonymous
i see there is lot of difference between, "if" and "only if"

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