मराठी

Let S = {A, B, C}. Find the Total Number of Binary Operations on S. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

Number of binary operations on a set with n elements is `n^(n^2)`

Here, S = {abc}
Number of elements in S = 3
Number of binary operations on a set with 3 elements is `3^(3^2) = 3^9`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Binary Operations - Exercise 3.1 [पृष्ठ ५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 3 Binary Operations
Exercise 3.1 | Q 5 | पृष्ठ ५

संबंधित प्रश्‍न

Show that the binary operation * on A = R – { – 1} defined as a*b = a + b + ab for all a, b ∈ A is commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible.


Consider a binary operation * on defined as a3 + b3. Choose the correct answer.

(A) Is * both associative and commutative?

(B) Is * commutative but not associative?

(C) Is * associative but not commutative?

(D) Is * neither commutative nor associative?


Given a non-empty set X, let *: P(X) × P(X) → P(X) be defined as A * B = (A − B) ∪ (B −A), &mnForE; AB ∈ P(X). Show that the empty set Φ is the identity for the operation * and all the elements A of P(X) are invertible with A−1 = A. (Hint: (A − Φ) ∪ (Φ − A) = Aand (A − A) ∪ (A − A) = A * A = Φ).


Determine whether the following operation define a binary operation on the given set or not :

\[' * ' \text{on Q defined by } a * b = \frac{a - 1}{b + 1} \text{for all a, b} \in Q .\]


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.


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.


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


 Check the commutativity and associativity of the following binary operation'*' on Q defined by a * b = ab + 1 for all a, b ∈ Q ?


If the binary operation o is defined by aob = a + b − ab on the set Q − {−1} of all rational numbers other than 1, shown that o is commutative on Q − [1].


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


On the set Z of integers, if the binary operation * is defined by a * b = a + b + 2, then find the identity element.


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 * be a binary operation on Q − {−1} defined by a * b = a + b + ab for all a, b ∈ Q − {−1} Show that '*' is both commutative and associative on Q − {−1}.


Write the total number of binary operations on a set consisting of two elements.


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


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 ________________ .


Q+ is the set of all positive rational numbers with the binary operation * defined by \[a * b = \frac{ab}{2}\] for all ab ∈ Q+. The inverse of an element a ∈ Q+ is ______________ .


Which of the following is true ?


The binary operation * defined on N by a * b = a + b + ab for all a, b N is ________________ .


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


Examine whether the operation *defined on R by a * b = ab + 1 is (i) a binary or not. (ii) if a binary operation, is it associative or not?


Fill in the following table so that the binary operation * on A = {a, b, c} is commutative.

* a b c
a b    
b c b a
c a   c

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) ∧ C


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 existence of an identity, the existence of inverse properties for the operation * on A


Choose the correct alternative:

In the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R?


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

a * b = a – b for a, b ∈ Q


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

a * b = a – b + ab for a, b ∈ Q


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

a * b = a + ab ∀ a, b ∈ Q


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

a * b = (a – b)2 ∀ a, b ∈ Q


Let * be binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R. Then the operation * is ______.


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


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 binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is ____________.


a * b = `((a + b))/2` ∀a, b ∈ N is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×