English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

Choose the correct alternative: If a * b = aba2+b2 on the real numbers then * is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

If a * b = `sqrt("a"^2 + "b"^2)` on the real numbers then * is

Options

  • Commutative but not associative

  • Associative but not commutative

  • Both commutative and associative

  • Neither commutative nor associative

MCQ

Solution

Both commutative and associative

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Discrete Mathematics - Exercise 12.3 [Page 249]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 12 Discrete Mathematics
Exercise 12.3 | Q 7 | Page 249

RELATED QUESTIONS

Let * be the binary operation on given by a * = L.C.M. of and b. Find

(i) 5 * 7, 20 * 16

(ii) Is * commutative?

(iii) Is * associative?

(iv) Find the identity of * in N

(v) Which elements of are invertible for the operation *?


Find which of the operations given above has identity.


Let A = × and * be the binary operation on A defined by  (ab) * (cd) = (cd)

Show that * is commutative and associative. Find the identity element for * on A, if any.


Determine whether the following operation define a binary operation on the given set or not : 'O' on Z defined by a O b = ab for all a, b ∈ Z.


Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On Z+, defined * by a * b = a − b

Here, Z+ denotes the set of all non-negative integers.


Let * be a binary operation on the set I of integers, defined by a * b = 2a + b − 3. Find the value of 3 * 4.


Let S = {abc}. Find the total number of binary operations on S.


On Q, the set of all rational numbers, * is defined by \[a * b = \frac{a - b}{2}\] , shown that * is no associative ?


The binary operation * is defined by \[a * b = \frac{ab}{7}\] on the set Q of all rational numbers. Show that * is associative.


Define a binary operation on a set.


Write the inverse of 5 under multiplication modulo 11 on the set {1, 2, ... ,10}.


If a * b = a2 + b2, then the value of (4 * 5) * 3 is _____________ .


On the power set P of a non-empty set A, we define an operation ∆ by

\[X ∆ Y = \left( \overline{X} \cap Y \right) \cup \left( X \cap \overline{Y} \right)\]

Then which are of the following statements is true about ∆.


For the binary operation * defined on R − {1} by the rule a * b = a + b + ab for all a, b ∈ R − {1}, the inverse of a is ________________ .


Determine whether * is a binary operation on the sets-given below.

a * b = min (a, b) on A = {1, 2, 3, 4, 5}


Let A = `((1, 0, 1, 0),(0, 1, 0, 1),(1, 0, 0, 1))`, B = `((0, 1, 0, 1),(1, 0, 1, 0),(1, 0, 0, 1))`, C = `((1, 1, 0, 1),(0, 1, 1, 0),(1, 1, 1, 1))` be any three boolean matrices of the same type. Find A v B


Let * be a binary operation defined on Q. Find which of the following binary operations are associative

a * b = ab2 for a, b ∈ Q


A binary operation A × A → is said to be associative if:-


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×