Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
उत्तर
This statement is False.
APPEARS IN
संबंधित प्रश्न
Let * be a binary operation, on the set of all non-zero real numbers, given by `a** b = (ab)/5` for all a,b∈ R-{0} that 2*(x*5)=10
Let A = Q ✕ Q, where Q is the set of all rational numbers, and * be a binary operation defined on A by (a, b) * (c, d) = (ac, b + ad), for all (a, b) (c, d) ∈ A.
Find
(i) the identity element in A
(ii) the invertible element of A.
(iii)and hence write the inverse of elements (5, 3) and (1/2,4)
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 a ∗ b = a – b
For each binary operation * defined below, determine whether * is commutative or associative.
On Q, define a * b = ab + 1
State whether the following statements are true or false. Justify.
For an arbitrary binary operation * on a set N, a * a = ∀ a a * N.
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 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.
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.
Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer.
Find the total number of binary operations on {a, b}.
Determine which of the following binary operations are associative and which are commutative : * on Q defined by \[a * b = \frac{a + b}{2} \text{ for all a, b } \in Q\] ?
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 a, b ∈ R ?
Construct the composition table for ×6 on set S = {0, 1, 2, 3, 4, 5}.
Find the inverse of 5 under multiplication modulo 11 on Z11.
On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all a, b ∈ Z. Write the inverse of 4.
Write the composition table for the binary operation multiplication modulo 10 (×10) on the set S = {2, 4, 6, 8}.
A binary operation * is defined on the set R of all real numbers by the rule \[a * b = \sqrt{ a^2 + b^2} \text{for all a, b } \in R .\]
Write the identity element for * on R.
Let * be a binary operation on N given by a * b = HCF (a, b), a, b ∈ N. Write the value of 22 * 4.
If the binary operation * on Z is defined by a * b = a2 − b2 + ab + 4, then value of (2 * 3) * 4 is ____________ .
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 ________________ .
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is _________________ .
Determine whether * is a binary operation on the sets-given below.
a * b – a.|b| on R
Define an operation * on Q as follows: a * b = `(("a" + "b")/2)`; a, b ∈ Q. Examine the closure, commutative and associate properties satisfied by * on Q.
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
Choose the correct alternative:
Which one of the following is a binary operation on N?
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
A binary operation A × A → is said to be associative if:-