Advertisements
Advertisements
प्रश्न
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?
विकल्प
a * b = min(a.b)
a * b = max(a, b)
a * b = a
a * b = ab
उत्तर
a * b = ab
APPEARS IN
संबंधित प्रश्न
Consider a binary operation * on N defined as a * b = 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?
Let A = Q x Q and let * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for (a, b), (c, d) ∈ A. Determine, whether * is commutative and associative. Then, with respect to * on A
1) Find the identity element in A
2) Find the invertible elements of A.
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 :
\[' * ' \text{on Q defined by } a * b = \frac{a - 1}{b + 1} \text{for all a, b} \in Q .\]
Let * be a binary operation on the set I of integers, defined by a * b = 2a + b − 3. Find the value of 3 * 4.
On the set Z of integers a binary operation * is defined by a * b = ab + 1 for all a , b ∈ Z. Prove that * is not associative on Z.
Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.
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 ?
Construct the composition table for +5 on set S = {0, 1, 2, 3, 4}.
Write the composition table for the binary operation ×5 (multiplication modulo 5) on the set S = {0, 1, 2, 3, 4}.
Q+ denote the set of all positive rational numbers. If the binary operation a ⊙ on Q+ is defined as \[a \odot = \frac{ab}{2}\] ,then the inverse of 3 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 ____________ .
Which of the following is true ?
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is _________________ .
An operation * is defined on the set Z of non-zero integers by \[a * b = \frac{a}{b}\] for all a, b ∈ Z. Then the property satisfied is _______________ .
Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N 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 = {a + `sqrt(5)`b : a, b ∈ Z}. Check whether the usual multiplication is a binary operation on A
In the set N of natural numbers, define the binary operation * by m * n = g.c.d (m, n), m, n ∈ N. Is the operation * commutative and associative?
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
