Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > A binary operationon a set of integers is def...
Start Learning for Free
A binary operation 
on a set of integers is defined as x y = x2 + y2. Which one of the following statements is TRUE about ?
on a set of integers is defined as x y = x2 + y2. Which one of the following statements is TRUE about ?- a)Commutative but not associative
- b)Both commutative and associative
- c)Associative but not commutative
- d)Neither commutative nor associative
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A binary operationon a set of integers is defined as xy = x2+ y2. Whic...
The binary operation ⊕ defined as : x⊕y = x2 + y2 is commutative as
y⊕x = y2 + x2 = x⊕y
However , it is not associative as is illustrated below:
x⊕(y⊕z) = x2 + (y2 + z2)2 and
(x⊕y)⊕z = (x2 + y2)2 +z2
Hence we can clearly see that x⊕(y⊕z) ≠ (x⊕y)⊕z
Hence the binary operation ⊕ is commutative but not associative.
Most Upvoted Answer
A binary operationon a set of integers is defined as xy = x2+ y2. Whic...
Associativity: A binary operation ∗ on a set S is said to be associative if it satisfies the associative law: a ∗ (b ∗c) = (a ∗b) ∗c for all a, b, c ∈S.
Commutativity: A binary operation ∗ on a set S is said to be commutative if it satisfies the condition: a ∗b=b ∗a for all a, b, ∈S. In this case, the order in which elements are combined does not matter.
Solution: Here a binary operation on a set of integers is defined as x ⊕ y = x2 + y2. for Commutativity: x ⊕ y= y ⊕ x. LHS=> x ⊕ y= x^2+ y^2 RHS=> y ⊕ x= y^2+x^2 LHS = RHS. hence commutative. for Associativity: x ⊕ (y ⊕ z) =(x ⊕ y) ⊕ z LHS=> x ⊕ (y ⊕ z) = x ⊕ ( y^2+z^2)= x^2+(y^2+z^2)^2 RHS=> (x ⊕ y) ⊕ z= ( x^2+y^2) ⊕ z=(x^2+y^2)^2+z^2 So, LHS ≠ RHS, hence not associative.
Commutativity: A binary operation ∗ on a set S is said to be commutative if it satisfies the condition: a ∗b=b ∗a for all a, b, ∈S. In this case, the order in which elements are combined does not matter.
Solution: Here a binary operation on a set of integers is defined as x ⊕ y = x2 + y2. for Commutativity: x ⊕ y= y ⊕ x. LHS=> x ⊕ y= x^2+ y^2 RHS=> y ⊕ x= y^2+x^2 LHS = RHS. hence commutative. for Associativity: x ⊕ (y ⊕ z) =(x ⊕ y) ⊕ z LHS=> x ⊕ (y ⊕ z) = x ⊕ ( y^2+z^2)= x^2+(y^2+z^2)^2 RHS=> (x ⊕ y) ⊕ z= ( x^2+y^2) ⊕ z=(x^2+y^2)^2+z^2 So, LHS ≠ RHS, hence not associative.
Another Solution : [Tex]oplus[/Tex] commutative as x[Tex]oplus[/Tex]y is always same as y[Tex]oplus[/Tex]x. [Tex]oplus[/Tex] is not associative as (x[Tex]oplus[/Tex]y)[Tex]oplus[/Tex]z is (x^2 + y^2)^2 + z^2, but x[Tex]oplus[/Tex](y[Tex]oplus[/Tex]z) is x^2 + (y^2 + z^2)^2.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer?
Question Description
A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer?.
A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A binary operationon a set of integers is defined as xy = x2+ y2. Which one of the following statements is TRUE about?a)Commutative but not associativeb)Both commutative and associativec)Associative but not commutatived)Neither commutative nor associativeCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup