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हिंदी

Select the correct answer from given alternative. The relation ">" in the set of N (Natural number) is

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प्रश्न

Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) is

विकल्प

  • Symmetric

  • Reflexive

  • Transitive

  • Equivalence relation

MCQ
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उत्तर

The relation ">" in the set of N (Natural number) is Transitive

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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. (7) | 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.


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 = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.

 

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


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

(ii) (ab) R (cd) ⇒ (cd) R (ab) for all (ab), (cd) ∈ N × N

 

 


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.


Let R = [(xy) : xy ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.


Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(xy) : x − yis odd}. Write R in roster form. 


If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =


Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R−1 is


If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation on Z, then the domain of R is ______.


Let R be a relation from a set A to a set B, then


If R is a relation on a finite set having n elements, then the number of relations on A is


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


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

R1 = {(a, a2)/a is prime number less than 15}


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

R3 = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}


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}


Select the correct answer from given alternative

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


Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R1 = {(1, 4), (1, 5), (1, 6)}


Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}


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}


A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M), and an Executive Officer (E). The company provides ₹ 10,000, ₹ 25,000, ₹ 50,000, and ₹ 1,00,000 as salaries to the people who work in the categories A, C, M, and E respectively. If A1, A2, A3, A4, and A5 were Assistants; C1, C2, C3, C4 were Clerks; M1, M2, M3 were managers and E1, E2 was Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram


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


Discuss the following relation for reflexivity, symmetricity and transitivity:

The relation R defined on the set of all positive integers by “mRn if m divides n”


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 equivalence


Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation


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 equivalence


Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?


Choose the correct alternative:

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


If R1 = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of R1.


Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.


If R = {(x, y): x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is ______.


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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