(COMPLICATED) Mass and time question?

Question

In relativity, If objects were to approach the speed of light, they would increase in mass, and slow down time for that object relative to those moving much slower...

IF: (A) increase in speed = (B) increase in mass
(A) increase in speed = (C) slowing of relative time

THEN : due to transitive property of mathematics, is (B) = (C)
possible? It corresponds to gravity being caused by
fourth dimension interference (ball on blanket example)
and Einstein's beliefs of time being the fourth dimension.

Answer 1

no, it's not.
increase in speed doesn't equal to an increase of mass.

here is a more complete version of the famous E = mc^2 that will help you understand the mistake.

E = (m * c^2) / sqrt ( 1 - v^2 / c^2 )

v = speed
c = speed of light (constant)
m = mass
E = energy

based on this, you see that an increase in speed = an increase in energy, and that the energy doesn't equal to the mass but is proportional to the mass.

only time and speed have a direct relationship, that is increase in speed = slowing of time.

Answer 2

I think it is not possible of slowing of relative time is the cause of increase in mass, if this happens, objects on earth which having mass much bigger than human mass will slow down, did you observed this phenomena before?
The increase in mass, slowing of relative time and decreasing in length is the effect of the increasing in speed, those effects is due to the cause, therefore you will not get effect due to effect.
(This is what I think, correct me if i am wrong.)

For the gravity and time, I am not sure about it, maybe need someone else to explain it.

Answer 3

You are mistaken about transitivity.
The transitive property is:
If A --> B and B --> C, then A --> C.

In your example the mistake can be illustrated by increasing the mass in another way - add rocks to the cart. This will not affect any clock on the cart. Technically, speed doesn't increase mass, but it does increase inertia.