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Select the correct answer from given alternative. A relation between A and B is - Mathematics and Statistics

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प्रश्न

Select the correct answer from given alternative.

A relation between A and B is

पर्याय

  • only A × B

  • an Universal set of A × B

  • an equivalent set of A × B

  • a subset of A × B

MCQ
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उत्तर

A relation between A and B is a subset of A × B

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Sets and Relations - Miscellaneous Exercise 5.1 [पृष्ठ १०४]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (8) | पृष्ठ १०४

संबंधित प्रश्‍न

Let A = {1, 2, 3, …, 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.


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?


Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.


Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.


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

(ii) R = {(xy), : xy ∈ N, x + 2y = 8}


Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(xy) : 3x − y = 0, where xy ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.


The adjacent figure shows a relationship between the sets P and Q. Write this relation in (i) set builder form (ii) roster form. What is its domain and range?


For the relation R1 defined on R by the rule (ab) ∈ R1 ⇔ 1 + ab > 0. Prove that: (ab) ∈ R1 and (b , c) ∈ R1 ⇒ (ac) ∈ R1 is not true for all abc ∈ R.


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.

 


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 ______.


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


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


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

R5 = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}


Select the correct answer from given alternative.

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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

R4 = {(4, 2), (2, 6), (5, 1), (2, 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:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is reflexive


Answer the following:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is symmentric


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 = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}


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

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


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

R2 = {(–1, 1)}


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)}


Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R


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 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


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


Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai


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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:

The rule f(x) = x2 is a bijection if the domain and the co-domain are given by


Is the following relation a function? Justify your answer

R1 = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`


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 ______.


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