मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Write the relation in the Roster Form. State its domain and range R1 = {(a, a2)/a is prime number less than 15}

Advertisements
Advertisements

प्रश्न

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

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

बेरीज
Advertisements

उत्तर

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

∴ a = 2, 3, 5, 7, 11, 13

∴ a2 = 4, 9, 25, 49, 121, 169

∴ R1 = {(2, 4), (3, 9), (5, 25), (7, 49), (11, 121), (13, 169)}

∴ Domain (R1)

= {a/a is a prime number less than 15}

= {2, 3, 5, 7, 11, 13}

Range (R1)

= {a2/a is a prime number less than 15}

= {4, 9, 25, 49, 121, 169}

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Sets and Relations - Exercise 5.2 [पृष्ठ १०३]

APPEARS IN

संबंधित प्रश्‍न

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.


Let A = {ab}. List all relations on A and find their number.

 

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.


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.


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 the set A has p elements, B has q elements, then the number of elements in A × B is


Select the correct answer from given alternative.

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

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

R2 = {(1, 5), (2, 4), (3, 6)}


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 symmentric


Answer the following:

Show that the following is an equivalence relation

R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}


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?

R3 = {(2, –1), (7, 7), (1, 3)}


Multiple Choice Question :

Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to B is ________.


Discuss the following relation for reflexivity, symmetricity and transitivity:

Let P denote the set of all straight lines in a plane. The relation R defined by “lRm if l is perpendicular to m”


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 symmetric


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


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


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


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 transitive


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 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?


Choose the correct alternative:

Let R be the universal relation on a set X with more than one element. Then R is


Choose the correct alternative:

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


Is the following relation a function? Justify your answer

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


If R3 = {(x, x) | x is a real number} is a relation. Then find domain and range of R3.


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

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


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

g = `"n", 1/"n" |"n"` is a positive integer


Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.


A function from set \(A\) to set \(B\) is a relation in which:


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


For \(A=\{-1,0,1\}\), which ordered pair is a remaining element of \(A\times A\) besides \((-1,0)\) and \((0,1)\)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×