The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+15 votes
1.2k views

A binary operation $\oplus$ on a set of integers is defined as $x \oplus y = x^{2}+y^{2}$. Which one of the following statements is TRUE about $\oplus$?
 

  1. Commutative but not associative
  2. Both commutative and associative
  3. Associative but not commutative
  4. Neither commutative nor associative
asked in Set Theory & Algebra by Boss (18k points)
edited by | 1.2k views

1 Answer

+30 votes
Best answer
Answer is (A) Commutative but not associative.

$y \oplus x = y^2 + x^2 = x \oplus y$. Hence, commutative.

$ (x \oplus y) \oplus z = (x^2 + y^2) \oplus z = (x^2 + y^2)^2 + z^2$
$ x \oplus (y \oplus z) = x \oplus (y^2 + z^2) = x^2 + (y^2 + z^2)^2$

So, $( (x \oplus y) \oplus z) \neq (x \oplus (y \oplus z))$, hence not associative.
answered by Veteran (353k points)
selected by
0

This Will Help ....



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

37,117 questions
44,700 answers
127,275 comments
43,761 users