Question

is (a-b)-c=a-(b-c) always, sometimes or never true? explain

Answer 1

try it with an example

a = 1
b = 2
c = 3

(1-2) - 3 = 1 - (2 - 3)

are they the same?

Answer 2

if we solve the brackets is L.H.S=R.H.S
a-b-c=a-b+c
are they same?

Answer 3

no, it is never true @Dobby1

Answer 4

addition is associative. subtraction is not.

Answer 5

it is true only if-c=c
or 0=2c
or c=0

Answer 6

Ok according to sujithayer, the answer is sometimes true.

Answer 7

i dont think it's possible for -c = c in any case

0 = 2c is the same as c = 0, and if c = 0 then it is irrelevant to the problem anyways

Answer 8

so, still never true lol

Answer 9

by the reasoning that subtraction is not associative (i.e., you cannot re-order the subtraction of numbers without flipping the sign of some numbers)

Answer 10

It is true you can't reorder it although 0 is a digit as well so it can be used and if that was to happen then the function should work. Although if it where digits that have values besides 0 then it can't happen therefore the answer is sometimes true.

Answer 11

@Osako yes that's true, but in the context of this problem I think the natural assumption is that c is any number not equal to zero.

As you see, by making c = 0, you are changing the context of this problem entirely. The form changes to a - b = a - b, which is always true. Adding (or subtracting) a 0 from both sides will obviously remain always true.

It is only when c is not equal to 0 that anything interesting happens. So, in short, I would consider this problem to never have any correct solutions, unless you are allowing zeros.