Annapanna
\(m ⊕ p =n\)
\(n ⊕ r =m \)
\(n ⊕ q =q \)
\(p ⊕ q =p \)
\(q ⊕ p =r \)
If the relations shown hold for the operation ⊕ and the numbers m, n, p, q, and r, then \([(m⊕p)⊕ q]⊕ p =\)
(A) m
(B) n
(C) p
(D) q
(E) r
Hi,
My answer was "p", because I got as far as m+p=n so
[(m+p) + q] + p = [n+q] + p.
Then I tried to see if I can express "n" or "q" with "p," so I looked over at the relations. I noticed n+q=q. Instead realizing that I should be using this equation to make (q + p), I thought, that this means n=0. Then I noticed that p+q=p. So q=0, too.
Therefore, (n+q) + p = 0 + p.
in addition, if q=0 then q+p=r means that r=p. I pretty sure I'm wrong but I don't see how and it gives me a headache. Can someone please explain why is this wrong?
The problem with your solution is that you mistake the ⊕ sign for addition. It's not; it's a function. Now, taking this into consideration, reread the question and review the solutions above. Hope it helps.