Can someone help me with the proof "if ab = ac, then b = c"
I've tried to solve this for a while now. I know you have to use the substitution, reflexive, and maybe transitive property of equality. Thanks in advance!
2006-09-13 11:32:25 · 4 answers · asked by ? 3 in Science & Mathematics ➔ Mathematics
let x be the inverse of a. Then xa = identity.
If ab=ac, then x(ab) = x(ac)
Therefore, (xa)b = (xa)c
and since xa = identity, it follows that b = c.
... yeah, the inverse should be a^-1, but that notation gets messy on line, so I just called it x. You get the idea.
I trust that helps :-)
2006-09-13 11:37:59 · answer #1 · answered by Bramblyspam 7 · 1⤊ 0⤋
to prove it you just divide both sides of ab=ac by a. Then the a will cancel thus b=c
2006-09-13 11:36:41 · answer #2 · answered by sley 2 · 0⤊ 0⤋
It's actually only true if a is not zero. The answers above divide by a, which you can't do if it is zero. You can also see that if a is zero, then any b and any c would give equality.
2006-09-13 11:56:56 · answer #3 · answered by Ken H 4 · 1⤊ 0⤋
ab=ac
b=ac/a
so reduce a
b=c
2006-09-13 11:34:45 · answer #4 · answered by greengrin 2 · 0⤊ 0⤋