हिंदी

Let * Be a Binary Operation on N Given by a * B = Hcf (A, B), A, B ∈ N. Write the Value of 22 * 4. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

Given: a * b = HCF (a, b)
Here,
22 * 4 = HCF (22, 4)
                    = 2                                [because highest common factor of 22 and 4 is 2]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Binary Operations - Exercise 3.6 [पृष्ठ ३६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 3 Binary Operations
Exercise 3.6 | Q 19 | पृष्ठ ३६

संबंधित प्रश्न

Determine whether or not of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this.

On Z+, define * by ab


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

On Z, define − b


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

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


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

If * is a commutative binary operation on N, then * (c) = (b) * a


Consider the binary operations*: ×→ and o: R × R → defined as a * b = |a - b| and ab = a, &mnForE;ab ∈ R. Show that * is commutative but not associative, o is associative but not commutative. Further, show that &mnForE;abc ∈ Ra*(b o c) = (ab) o (a * c). [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over *? Justify your answer.


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 − 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.


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


Determine which of the following binary operations are associative and which are commutative : * on Q defined by \[a * b = \frac{a + b}{2} \text{ for all a, b } \in Q\] ?


Let A be any set containing more than one element. Let '*' be a binary operation on A defined by a * b = b for all a, b ∈ A Is '*' commutative or associative on A ?


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


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 Z defined by a * b = a − b for all ab ∈ Z ?


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


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


On the set Q of all ration numbers if a binary operation * is defined by \[a * b = \frac{ab}{5}\] , prove that * is associative on Q.


Let * be a binary operation on Q − {−1} defined by a * b = a + b + ab for all a, b ∈ Q − {−1} Find the identity element in Q − {−1} ?


Let A = R0 × R, where R0 denote the set of all non-zero real numbers. A binary operation '⊙' is defined on A as follows (ab) ⊙ (cd) = (acbc + d) for all (ab), (cd) ∈ R0 × R :

Find the identity element in A ?

 


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 ?


Define a binary operation on a set.


Write the composition table for the binary operation ×5 (multiplication modulo 5) on the set S = {0, 1, 2, 3, 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 defined by a * b = 3a + 4b − 2. Find 4 * 5.


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


Let * be a binary operation on Q+ defined by \[a * b = \frac{ab}{100} \text{ for all a, b } \in Q^+\] The inverse of 0.1 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 * be a binary operation defined on Q. Find which of the following binary operations are associative

a * b = `"ab"/4` 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 – b ∀ a, b ∈ Q


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

a * b = a2 + b2 ∀ a, b ∈ Q


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


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 ____________.


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


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


Subtraction and division are not binary operation on.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×