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Select the correct answer from given alternative If A = {a, b, c} The total no. of distinct relations in A × A is

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प्रश्न

Select the correct answer from given alternative

If A = {a, b, c} The total no. of distinct relations in A × A is

विकल्प

  • 3

  • 9

  • 8

  • 29 

MCQ
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उत्तर

If A = {a, b, c} The total no. of distinct relations in A × A is 29 

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अध्याय 5: Sets and Relations - Miscellaneous Exercise 5.1 [पृष्ठ १०४]

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बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
अध्याय 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (10) | पृष्ठ १०४

संबंधित प्रश्न

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.


The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`

The relation g is defined by  g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`

Show that f is a function and g is not a function.


Let A = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.


Determine the domain and range of the relation R defined by

(i) R = [(x, x + 5): x ∈ (0, 1, 2, 3, 4, 5)]


Let A = (x, y, z) and B = (a, b). Find the total number of relations from A into B.

 

Define a relation R on the set N of natural number by R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.


If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x2 + y2 = 9, then write domain of R.


Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B


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Answer the following:

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Answer the following:

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Answer the following:

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R1 = {(2, 1), (7, 1)}


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Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

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Discuss the following relation for reflexivity, symmetricity and transitivity:

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Discuss the following relation for reflexivity, symmetricity and transitivity:

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Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it symmetric


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Choose the correct alternative:

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Choose the correct alternative:

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is


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Is the given relation a function? Give reasons for your answer.

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If \(R\) is a relation from \(A\) to \(B\), what is its co-domain?


Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \((A\times B)\cap(A\times C)\)?


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