हिंदी

Write the Inverse of 5 Under Multiplication Modulo 11 on the Set {1, 2, ... ,10}. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

As, e = 1 : 5 × 9 ≡ 1 (mod 11)

So, the inverse of 5 i.e. 5 - 1 = 9

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Binary Operations - Exercise 3.6 [पृष्ठ ३५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 3 Binary Operations
Exercise 3.6 | Q 9 | पृष्ठ ३५

संबंधित प्रश्न

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

On Z+, define = 2ab


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.


Find the total number of binary operations on {ab}.


Check the commutativity and associativity of the following binary operations '*'. on N defined by a * b = 2ab for all a, b ∈ N ?


Check the commutativity and associativity of the following binary operation  '*' on R defined by a * b = a + b − 7 for all ab ∈ R ?


Show that the binary operation * on Z defined by a * b = 3a + 7b is not commutative ?


Let S be the set of all real numbers except −1 and let '*' be an operation defined by a * b = a + b + ab for all ab ∈ S. Determine whether '*' is a binary operation on S. If yes, check its commutativity and associativity. Also, solve the equation (2 * x) * 3 = 7.


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


Find the identity element in the set of all rational numbers except −1 with respect to *defined by a * b = a + b + ab.


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

Show that 'o' is both commutative and associate ?


Let R0 denote the set of all non-zero real numbers and let A = R0 × R0. If '*' is a binary operation on A defined by

(a, b) * (c, d) = (ac, bd) for all (a, b), (c, d) ∈ A

Find the invertible element in A ?


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


On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all ab ∈ Z. Write the inverse of 4.


Define a binary operation on a set.


Let * be a binary operation, on the set of all non-zero real numbers, given by \[a * b = \frac{ab}{5} \text { for all a, b } \in R - \left\{ 0 \right\}\]

Write the value of x given by 2 * (x * 5) = 10.


For the binary operation multiplication modulo 5 (×5) defined on the set S = {1, 2, 3, 4}. Write the value of \[\left( 3 \times_5 4^{- 1} \right)^{- 1}.\] 


Write the composition table for the binary operation ×5 (multiplication modulo 5) on the set S = {0, 1, 2, 3, 4}.


If the binary operation * on the set Z of integers is defined by a * b = a + 3b2, find the value of 2 * 4.


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 ∆.


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 ________________ .


If a binary operation * is defined on the set Z of integers as a * b = 3a − b, then the value of (2 * 3) * 4 is ___________ .


The law a + b = b + a is called _________________ .


A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is ________________ .


Consider the binary operation * defined on Q − {1} by the rule
a * b = a + b − ab for all a, b ∈ Q − {1}
The identity element in Q − {1} is _______________ .


The number of binary operation that can be defined on a set of 2 elements is _________ .


Let M = `{{:((x, x),(x, x)) : x ∈ "R"- {0}:}}` and let * be the matrix multiplication. Determine whether M is closed under *. If so, examine the commutative and associative properties satisfied by * on M


Let A be Q\{1} Define * on A by x * y = x + y – xy. Is * binary on A? If so, examine the commutative and associative properties satisfied by * on A


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


Let N be the set of natural numbers. Then, the binary operation * in N defined as a * b = a + b, ∀ a, b ∈ N has identity element.


The identity element for the binary operation * defined on Q ~ {0} as a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} is ______.


Let * be a binary operation on Q, defined by a * b `= (3"ab")/5` is  ____________.


Let * be a binary operation on set Q of rational numbers defined as a * b `= "ab"/5`. Write the identity for * ____________.


Let A = N x N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is ____________.


The identity element for the binary operation * defined on Q – {0} as a * b = `"ab"/2 AA  "a, b" in "Q" - {0}` is ____________.


If * is a binary operation on the set of integers I defined by a * b = 3a + 4b - 2, then find the value of 4 * 5.


Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×