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Choose the correct alternative: A binary operation on a set S is a function from - Mathematics

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प्रश्न

Choose the correct alternative:

A binary operation on a set S is a function from

पर्याय

  • S → S

  • (S × S) → S

  • S → (S × S)

  • (S × S) → (S × S)

MCQ

उत्तर

(S × S) → S

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Discrete Mathematics - Exercise 12.3 [पृष्ठ २४९]

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

संबंधित प्रश्‍न

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

On − {−1}, define `a*b = a/(b+1)`


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 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


Check the commutativity and associativity of the following binary operation 'o' on Q defined by \[\text{a o b }= \frac{ab}{2}\] for all a, b ∈ Q ?


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


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 ?


Define an associative binary operation on a set.


Let * be a binary operation, on the set of all non-zero real numbers, given by \[a * b = \frac{ab}{5} \text { for all a, b } \in R - \left\{ 0 \right\}\]

Write the value of x given by 2 * (x * 5) = 10.


Write the composition table for the binary operation ×5 (multiplication modulo 5) on the set S = {0, 1, 2, 3, 4}.


Let * be a binary operation defined by a * b = 3a + 4b − 2. Find 4 * 5.


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 defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is ____________ .


Let '*' be a binary operation on N defined by
a * b = 1.c.m. (a, b) for all a, b ∈ N
Find 2 * 4, 3 * 5, 1 * 6.


If * is defined on the set R of all real numbers by *: a*b = `sqrt(a^2 + b^2 ) `, find the identity elements, if it exists in R with respect to * .


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 v B) ∧ 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 commutative and associative properties satisfied by * on M


A binary operation on a set has always the identity element.


Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. Find 2 * `1/3`.


Subtraction and division are not binary operation on.


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