## sara12345 2 years ago Logic

1. sara12345

|dw:1348907509327:dw|

2. sara12345

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

3. sara12345

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"?

5. sara12345

no, the thing troubling me is "only if"

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

7. sara12345

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

8. sara12345

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.

10. sara12345

|dw:1348907860375:dw|

"A square cannot be a rectangle"?

12. sara12345

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

13. sara12345

only if its b, then only it can be a

14. UnkleRhaukus

"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.

16. sara12345

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.

20. sara12345

@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.

22. sara12345

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

23. sara12345

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

24. sara12345

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

25. UnkleRhaukus

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

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.

28. sara12345

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

29. sara12345

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

30. zzr0ck3r

@sara12345 do you understand if a then b?

31. UnkleRhaukus

if and only if $$\Leftrightarrow$$ iff

32. sara12345

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

33. zzr0ck3r

34. sara12345

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

35. sara12345

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

36. sara12345

il start over.

37. UnkleRhaukus

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

38. sara12345

ohh yea they say same thing, a->b

39. UnkleRhaukus

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

40. sara12345

so hw can iu break it meanigfully

41. sara12345

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

42. sara12345

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