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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? - Mathematics

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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?

पर्याय

  • a * b = min(a.b)

  • a * b = max(a, b)

  • a * b = a

  • a * b = ab

MCQ

उत्तर

a * b = ab

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पाठ 12: Discrete Mathematics - Exercise 12.3 [पृष्ठ २४९]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 12 Discrete Mathematics
Exercise 12.3 | Q 4 | पृष्ठ २४९

संबंधित प्रश्‍न

Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table.

(i) Compute (2 * 3) * 4 and 2 * (3 * 4)

(ii) Is * commutative?

(iii) Compute (2 * 3) * (4 * 5).

(Hint: use the following table)

* 1 2 3 4 5
1 1 1 1 1 1
2 1 2 1 2 1
3 1 1 3 1 1
4 1 2 1 4 1
5 1 1 1 1 5

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 :

\[' * ' \text{on Q defined by } a * b = \frac{a - 1}{b + 1} \text{for all a, b} \in Q .\]


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 ?


If the binary operation o is defined by aob = a + b − ab on the set Q − {−1} of all rational numbers other than 1, shown that o is commutative on Q − [1].


On the set Q of all ration numbers if a binary operation * is defined by \[a * b = \frac{ab}{5}\] , prove that * is associative on Q.


Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Show that '*' is both commutative and associative ?


Let * be a binary operation on Q − {−1} defined by a * b = a + b + ab for all a, b ∈ Q − {−1} Find the identity element in 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 :

Find the invertible elements in A ?


Construct the composition table for ×5 on Z5 = {0, 1, 2, 3, 4}.


On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all ab ∈ Z. Write the inverse of 4.


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


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 ________________ .


Q+ is the set of all positive rational numbers with the binary operation * defined by \[a * b = \frac{ab}{2}\] for all ab ∈ Q+. The inverse of an element a ∈ Q+ 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 defined on Q. Find which of the following binary operations are associative

a * b = ab2 for a, b ∈ Q


Let * be the binary operation defined on Q. Find which of the following binary operations are commutative

a * b = (a – b)2 ∀ a, b ∈ Q


The identity element for the binary operation * defined on Q ~ {0} as a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} is ______.


Let * be a binary operation on Q, defined by a * b `= (3"ab")/5` is  ____________.


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


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