हिंदी

If the Binary Operation * on the Set Z of Integers is Defined by a * B = a + 3b2, Find the Value of 2 * 4. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

Given: a * b = a + 3b2

Here,
         2 * 4 = 2 + 3 (4)2
                  = 2 + 3 (16)
                  = 2 + 48
                  = 50

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 18 | पृष्ठ ३६

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.


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

On Z, define − b


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

On Z+, define ab


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 : '*' on N defined by a * b = a + b - 2 for all a, b ∈ N


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

\[' +_6 ' \text{on S} = \left\{ 0, 1, 2, 3, 4, 5 \right\} \text{defined by}\] 
\[a +_6 b = \begin{cases}a + b & ,\text{ if a} + b < 6 \\ a + b - 6 & , \text{if a} + b \geq 6\end{cases}\]


Determine whether the following operation define a binary operation on the given set or not : '⊙' on N defined by a ⊙ b= ab + ba for all a, b ∈ N


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 R, define * by a * b = a + 4b2

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


Determine which of the following binary operation is associative and which is commutative : * on N defined by a * b = 1 for all a, b ∈ N ?


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


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


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

Find the invertible elements in A ?


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.


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 ?


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 ?


Write the identity element for the binary operation * on the set R0 of all non-zero real numbers by the rule \[a * b = \frac{ab}{2}\] for all ab ∈ R0.


Define a commutative binary operation on a set.


Which of the following is true ?


On Z an operation * is defined by a * b = a2 + b2 for all a, b ∈ Z. The operation * on Z is _______________ .


Let * be a binary operation on N defined by a * b = a + b + 10 for all ab ∈ N. The identity element for * in N is _____________ .


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 ___________________ .


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


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?


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 ∧ B) v 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 existence of identity, existence of inverse properties for the operation * 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


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 = `"ab"/4` for a, b ∈ Q.


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


The binary operation * defined on set R, given by a * b `= "a+b"/2` for all a, b ∈ R is ____________.


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


a * b = `((a + b))/2` ∀a, b ∈ N is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×