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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 - Mathematics and Statistics

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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

उत्तर

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

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Sets and Relations - Miscellaneous Exercise 5.1 [पृष्ठ १०४]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard 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 given figure shows a relationship between the sets P and Q. Write this relation

  1. in set-builder form.
  2. in roster form.

What is its domain and range?


Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.


Find the inverse relation R−1 in each of the cases:

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}


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


Let A = (xyz) and B = (ab). Find the total number of relations from A into B.

 

Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Is the statement true?

(a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R

Justify your answer in case.


Let R be a relation on N × N defined by
(ab) R (cd) ⇔ a + d = b + c for all (ab), (cd) ∈ N × N

(iii) (ab) R (cd) and (cd) R (ef) ⇒ (ab) R (ef) for all (ab), (cd), (ef) ∈ N × N

 

If R = {(xy) : xy ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.


If R is a relation from set A = (11, 12, 13) to set B = (8, 10, 12) defined by y = x − 3, then write R−1.

 


A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is


A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?

 

If R is a relation from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is


If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y


If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B


Express {(x, y) / x2 + y2 = 100, where x, y ∈ W} as a set of ordered pairs


Write the relation in the Roster Form. State its domain and range

R2 = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`


Write the relation in the Roster Form. State its domain and range

R4 = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}


Write the relation in the Roster Form. State its domain and range

R6 = {(a, b)/a ∈ N, a < 6 and b = 4}


Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}


Answer the following:

Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.


Answer the following:

Show that the following is an equivalence relation

R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}


Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R3 = {(2, –1), (7, 7), (1, 3)}


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

{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}


Multiple Choice Question :

If there are 1024 relation from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is


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


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


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 transitive


On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it  is reflexive


On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is equivalence


Choose the correct alternative:

Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is


Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.


Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.


Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?

f is a function from A to B

Justify your answer in case.


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