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