## the function of "only when"

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Seldom12121

Posts: 2
Joined: Thu Sep 28, 2017 8:22 am

### the function of "only when"

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?

Deardevil

Posts: 496
Joined: Sat Jun 04, 2016 11:00 pm

### Re: the function of "only when"

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

Posts: 63
Joined: Tue Aug 22, 2017 8:15 pm

### Re: the function of "only when"

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

somethingElse

Posts: 4007
Joined: Sat Jul 04, 2015 1:09 pm

### Re: the function of "only when"

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'

Deardevil

Posts: 496
Joined: Sat Jun 04, 2016 11:00 pm

### Re: the function of "only when"

"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.