PCP is undecidable.
We have to reduce PCP to X to show that X is undecidable.
If A is reducible to B we can use a solution to B to solve A.
For example :
P : Ram can lift 5 KG dumble.
Q : Ram can lift 2 KG dumble.
Here Q is reducible to P, that is if we know Ram can lift 5 KG dumble, it means Ram can lift any dumble of weight less than or equal to 5 KG as lifting lighter dumble is an easier task than lifting a heavy dumble.
So we can say that Ram can lift 2 KG Dumble given he can lift 5 KG Dumble.
P is a harder task than Q.
But note that P is not reducible to Q as the capability of lifting 2 KGs does not implies the capability of lifting 5 KGs.
Now consider another case,
M : Ram can not lift 5 KG Dumble.
N : Ram can not lift 2 KG Dumble.
Here M is reducible to N, that is if we know that Ram can not lift 2 KG Dumble then we can guarantee that he can not lift 5KG Dumble and his lifting threshold must be less than 2 KG.
Also, N is not reducible to M as if given Ram can not lift 5KGs we can not say anything about whether he would be able to lift 2 KGs or not.
Similarly in terms of Decidability of problems, we can say that
Decidability = Ram can lift ___ KG Dumble
Undecidability = Ram can not lift ___ KG Dumble
For convenience you may make following assumptions:
1) A is reducible to B is like saying problem A is easier than problem B.
2) Decidability of a Problem is directly proportional to its easiness: So easy problems are more likely to be decidable then the harder ones.
3) If a problem X is known to be decidable then every problem easier than X will also be decidable.
4) If a problem X is known to be undecidable then every problem harder than X will also be undecidable.
Now consider the following four cases:
(i) If A is reducible to B and B is decidable then A must also be decidable: we know that B is decidable so we can say that A is also decidable as A is easier than B.
(ii) If A is reducible to B and B is undecidable then A may or may not be decidable: B is undecidable but A is easier than B so we can not say that A is undecidable.
(iii) If A is reducible to B and A is decidable than B may or may not be decidable: A is known to be decidable but since B is harder than A we can not say anything about its decidability.
(iv)If A is reducible to B and A is undecidable then for sure B is also undecidable: A is known to be undecidable, and it is easier than B so every problem harder than A will also be undecidable.
Your question is similar to case (iv) here.
You can also check a previous GATE question based on the same concept here: https://gateoverflow.in/1375/gateoverflow.in
