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Select the correct answer from given alternative. If (x, y) ∈ R × R, then xy = x2 is a relation which is - Mathematics and Statistics

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प्रश्न

Select the correct answer from given alternative.

If (x, y) ∈ R × R, then xy = x2 is a relation which is

विकल्प

  • Symmetric

  • Reflexive

  • Transitive

  • Equivalence

MCQ
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उत्तर

If (x, y) ∈ R × R, then xy = x2 is a relation which is Equivalence

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अध्याय 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
अध्याय 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (9) | पृष्ठ १०४

संबंधित प्रश्न

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?


Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.

  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.

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


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 = {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 relation from A to B

Justify your answer in case.


Determine the domain and range of the relations:

(i) R = {(ab) : a ∈ N, a < 5, b = 4}


Determine the domain and range of the relations:

(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and}  \left| a \right| \leq 3 \right\}\]

 


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 implies (b, a) ∈ R

Justify your answer in case.


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.


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

 

 


If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).


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 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


If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is


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


Let R be a relation on N defined by x + 2y = 8. The 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


Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∩ C) = (A × B) ∩ (A × C)


Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)


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

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


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

R8 = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}


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

R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}


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:

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


Answer the following:

Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an 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?

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


Multiple Choice Question :

The range of the relation R = {(x, x2) | x is a prime number less than 13} 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 transitive


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 reflexive


Choose the correct alternative:

The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one of the following is true?


Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.


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

f = {(x, x) | x is a real number}


Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.


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