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Choose the correct alternative: Which one of the following is a binary operation on N ? - Mathematics

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प्रश्न

Choose the correct alternative:

Which one of the following is a binary operation on N?

विकल्प

  • Subtraction

  • Multiplication

  • Division

  • All the above

MCQ

उत्तर

Multiplication

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Discrete Mathematics - Exercise 12.3 [पृष्ठ २४९]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 12 Discrete Mathematics
Exercise 12.3 | Q 3 | पृष्ठ २४९

संबंधित प्रश्न

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

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


Given a non-empty set X, consider the binary operation *: P(X) × P(X) → P(X) given by A * B = A ∩ B &mnForE; AB in P(X) is the power set of X. Show that is the identity element for this operation and is the only invertible element in P(X) with respect to the operation*.


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


Determine whether the following operation define a binary operation on the given set or not : '×6' on S = {1, 2, 3, 4, 5} defined by

a ×6 b = Remainder when ab is divided by 6.


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.


Prove that the operation * on the set

\[M = \left\{ \begin{bmatrix}a & 0 \\ 0 & b\end{bmatrix}; a, b \in R - \left\{ 0 \right\} \right\}\] defined by A * B = AB is a binary operation.


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 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}.


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 :

Show that '⊙' is commutative and associative on A ?


Construct the composition table for ×4 on set S = {0, 1, 2, 3}.


Find the inverse of 5 under multiplication modulo 11 on Z11.


Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as \[a * b = \begin{cases}a + b & ,\text{ if a  + b} < 6 \\ a + b - 6 & , \text{if a + b} \geq 6\end{cases}\]

Show that 0 is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a.


Define a commutative binary operation on a set.


Define identity element for a binary operation defined on a set.


If a * b denote the bigger among a and b and if a ⋅ b = (a * b) + 3, then 4.7 = __________ .


Consider the binary operation * defined on the set A = {a, b, c, d} by the following table:

* a b c d
a a c b d
b d a b c
c c d a a
d d b a c

Is it commutative and associative?


Choose the correct alternative:

Subtraction is not a binary operation in


Choose the correct alternative:

If a * b = `sqrt("a"^2 + "b"^2)` on the real numbers then * is


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?


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


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