the function of "only when" Forum

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Seldom12121

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the function of "only when"

Post by Seldom12121 » Fri Nov 03, 2017 9:19 am

If the stem puts it that " A happens only when B happens", certainly we know that if A happens then B must happens. But I wonder here if B happens, must A happens? Take an example of the first sentence in PT18.S2.Q23, it says "Teachers are effective only when they help their students become independent learners." So according to it, if a teacher did help the students become independent learners, can we determine that the teacher is effective?
Beside I wonder is there any difference between the function of "only when" and "only if" in logical reasoning?
Can anyone here give his/her idea? :lol:

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Deardevil

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Re: the function of "only when"

Post by Deardevil » Fri Nov 03, 2017 9:47 am

If I tell you that all dogs are cute,
will knowing something is cute lead to that something being a pup?
Not really; cats are cute, horses are cute, hamsters are cute, dragons could be, etc.
So no, just by satisfying the necessary condition, we are unable to get the sufficient part as well.
And no, there is no logical difference between "only when" and "only if," as both indicate necessity.

barcafan202

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Re: the function of "only when"

Post by barcafan202 » Tue Nov 07, 2017 11:38 am

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Last edited by barcafan202 on Sun Nov 19, 2017 6:40 pm, edited 1 time in total.

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somethingElse

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Re: the function of "only when"

Post by somethingElse » Tue Nov 07, 2017 12:01 pm

If and only if and when and only when mean the same thing logically speaking. They both basically mean that the conditional relationship between the two statements is true regardless of which is the sufficient condition and which is the necessary.

E.g.:

A if and only if B means that A -> B is true and so is B -> A

I like pizza if and only if it has mushrooms

If the pizza has mushrooms -> I like it

If I like the pizza -> It has mushrooms

You can also just break it down like, 'A if B and A only if B'

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Deardevil

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Re: the function of "only when"

Post by Deardevil » Tue Nov 07, 2017 12:14 pm

"An animal is an herbivore IF and ONLY IF it eats plants."

H -> P
+
P -> H

How? The "if" is sufficient, so you write the first conditional.
The "only if" is necessary, so you write the second.

"If an animal is an herbivore, it only eats plants."

H -> P

"If an animal only eats plants, it is an herbivore."

P -> H

Combine these two to get, instead of one arrow, two arrows.

H <-> P

In this case, as long as you satisfy EITHER condition, the other also checks out.

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