हिंदी

Let * Be a Binary Operation on the Set I of Integers, Defined by a * B = 2a + B − 3. Find the Value of 3 * 4. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

Given: a * b = 2a + b − 3   
 3 * 4 = 2 (3) + 4 \[-\] 3

          = 6 + 4 \[-\] 3

           = 7

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Binary Operations - Exercise 3.1 [पृष्ठ ४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 3 Binary Operations
Exercise 3.1 | Q 3 | पृष्ठ ४

संबंधित प्रश्न

Let A = Q ✕ Q, where Q is the set of all rational numbers, and * be a binary operation defined on A by (a, b) * (c, d) =  (ac, b + ad), for all (a, b) (c, d) ∈ A.
Find
(i) the identity element in A
(ii) the invertible element of A.

(iii)and hence write the inverse of elements (5, 3) and (1/2,4)


For each binary operation * defined below, determine whether * is commutative or associative.

On Q, define a * b  = `(ab)/2`


Consider the binary operation ∨ on the set {1, 2, 3, 4, 5} defined by = min {ab}. Write the operation table of the operation∨.


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 *?


Let * be a binary operation on the set of rational numbers as follows:

(i) − 

(ii) a2 + b2

(iii) ab 

(iv) = (− b)2

(v) a * b = ab/4

(vi) ab2

Find which of the binary operations are commutative and which are associative.


State whether the following statements are true or false. Justify.

For an arbitrary binary operation * on a set N= ∀  N.


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 R, define by a*b = ab2

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


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+, define * by a * b = a

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


Prove that the operation * on the set

\[M = \left\{ \begin{bmatrix}a & 0 \\ 0 & b\end{bmatrix}; a, b \in R - \left\{ 0 \right\} \right\}\] defined by A * B = AB is a binary operation.


The binary operation * : R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4.


Check the commutativity and associativity of the following binary operation '*' on Q defined by a * b = ab2 for all ab ∈ Q ?


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


Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Show that '*' is both commutative and associative ?


Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Find the identity element in Z ?


Let 'o' be a binary operation on the set Q0 of all non-zero rational numbers defined by \[a o b = \frac{ab}{2}, \text{ for all a, b } \in Q_0\] :

 Find the identity element in Q0.


On R − {1}, a binary operation * is defined by a * b = a + b − ab. Prove that * is commutative and associative. Find the identity element for * on R − {1}. Also, prove that every element of R − {1} is invertible.


Let * be the binary operation on N defined by a * b = HCF of a and b.
Does there exist identity for this binary operation one N ?


Let A  \[=\] R  \[\times\] R and \[*\]  be a binary operation on defined by \[(a, b) * (c, d) = (a + c, b + d) .\] . Show that \[*\] is commutative and associative. Find the binary element for \[*\] on A, if any.


For the binary operation ×7 on the set S = {1, 2, 3, 4, 5, 6}, compute 3−1 ×7 4.


Let +6 (addition modulo 6) be a binary operation on S = {0, 1, 2, 3, 4, 5}. Write the value of \[2 +_6 4^{- 1} +_6 3^{- 1} .\]


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


If the binary operation * on Z is defined by a * b = a2 − b2 + ab + 4, then value of (2 * 3) * 4 is ____________ .


Mark the correct alternative in the following question:-

For the binary operation * on Z defined by a * b = a + b + 1, the identity element is ________________ .


Let * be a binary operation defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is ____________ .


The binary operation * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is equal to ______________ .


For the multiplication of matrices as a binary operation on the set of all matrices of the form \[\begin{bmatrix}a & b \\ - b & a\end{bmatrix}\] a, b ∈ R the inverse of \[\begin{bmatrix}2 & 3 \\ - 3 & 2\end{bmatrix}\] is ___________________ .


On the set Q+ of all positive rational numbers a binary operation * is defined by \[a * b = \frac{ab}{2} \text{ for all, a, b }\in Q^+\]. The inverse of 8 is _________ .


Let A = ℝ × ℝ and let * be a binary operation on A defined by (a, b) * (c, d) = (ad + bc, bd) for all (a, b), (c, d) ∈ ℝ × ℝ.
(i) Show that * is commutative on A.
(ii) Show that * is associative on A.
(iii) Find the identity element of * in A.


Let '*' be a binary operation on N defined by
a * b = 1.c.m. (a, b) for all a, b ∈ N
Find 2 * 4, 3 * 5, 1 * 6.


On Z, define * by (m * n) = mn + nm : ∀m, n ∈ Z Is * binary on Z?


Choose the correct alternative:

Which one of the following is a binary operation on N?


Is the binary operation * defined on Z (set of integer) by m * n = m – n + mn ∀ m, n ∈ Z commutative?


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

a * b = `"ab"/4` for a, b ∈ Q.


A binary operation on a set has always the identity element.


If the binary operation * is defined on the set Q + of all positive rational numbers by a * b = `" ab"/4. "Then"  3 "*" (1/5 "*" 1/2)` is equal to ____________.


Which of the following is not a binary operation on the indicated set?


Determine which of the following binary operation on the Set N are associate and commutaive both.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×