Discussion Problem_ (8)

[duck]

Let X and Y be statements. If we know that X implies Y, then we can also conclude that

(a)If Y is false, then X is false.
(b)X cannot be false.
(c)Y cannot be false.
(d)At least one of X and Y is true.
(e)X is true, and Y is also true.
(f)If X is false, then Y is false.
(g)If Y is true, then X is true.

[Mauli]

a).

[Sumit]

a)

[duck]

Well done! :)

Correct answer :(a)

[Ankit Agrawal]

Hi I am sorry but I am unable to get (a) as the correct option. When i started reading the options, I was convinced that the answer is (a). But when I reached the last option, I got a little confused. The anatomy of the first and the last options is the same. If Y is true/false, then X is true/false. Both of them, together, can be either correct or wrong. Now both of them cannot be correct, since only one option is correct. Hence, I decided to go along with the option (f).

I would really appreciate it if you could throw some light.

[ss]

@ankit
if X -> Y is true then
negation Y -> negation X will also be true.

also if X is false then no matter what Y is
X-> Y will be kind of vacuously true because the first part of the statement does not hold.

[duck]

@Ankit:
SS has correctly pointed out.
 
X implies Y means that if X is false, then Y can be true/false.
But, look at option(f): It only says that: If X is false, then Y is false.

Also, you can think of it in terms of necessary and sufficient conditions.
Y is a necessary condition for X.
It means if Y doesn't hold then X too won't hold.
So, we can perfectly infer option(a) from X implies Y.

[Akshay Jain]

but if we look at this problem from the perspective of development economics
In solow model, Growth effect implies Level effect in per capita income but Level effect does not imply Growth effect.
so e option goes with it. If X is true den Y is also true = if growth effect is true den level effect must be true...

[duck]

Hi akshay.. :)

option(e) says: X is true and Y is also true.
But, when X implies Y, we can have a case where X is false and Y is true.

[Erika]

two answers seemed correct to me.
a) and g)
After reading a few explanations I felt i was more sure that even g) was correct..if X implies Y and Y is true..then even x has to be true as a pre-condition; the same was as it has to be for a).
This is my logic..kindly clarify why we rule out g).
Thank you  

[duck]

If Y is true then X can be false also.
Thats why (g) is ruled out.