Let be the equivalence relation and A the set defined in Problem 4. Let Q be the
ID: 3142035 • Letter: L
Question
Let be the equivalence relation and A the set defined in Problem 4. Let Q be the set of equivalence classes; i e. Q = {a/b: (a, b) elementof A}, where a/b is the equivalence class [(a, b)]. We define multiplication on Q as follows: for all a/b, c/d elementof Q let a/b middot c/d. Since this definition involves equivalence relations, to see that it is well-defined, we need to make sure that it doesn't matter which element from the equivalence classes we use in our calculation; i.e. if a'/b' = a/b and c'/d' = c/d, then we hope that a/b middot c/d = a'/b' middot c'/d'. Towards this end, prove the following theorem: Theorem: If (a', b') (a, b) and (c', d') (c, d) then (a', b', b' d') (ac, bd).Explanation / Answer
Proof: a/b = a'/b' <=> ab' = a'b
AND c/d = c'/d' <=> cd' = c'd
=> (ac)(b'd') = (ab')(cd') = (a'b)(c'd) = (a'c')(bd)
<=> ac/bd = a'c'/b'd'.
Hope u got the answer,if u have any problem comment in here i will reply.
Thank you
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.