हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

R = {(x, x3): x is a prime number less than 10}

= {(x, x3) : X ∈ {2, 3, 5, 7})

 = {(2, 23), (3, 33), (5, 53), (7, 73)}

∴ R = {(2, 8), (3, 27), (5, 125), (7, 343)}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Relations and Functions - Exercise 2.2 [पृष्ठ ३६]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 2 Relations and Functions
Exercise 2.2 | Q 7 | पृष्ठ ३६
आरडी शर्मा Mathematics [English] Class 11
अध्याय 2 Relations
Exercise 2.3 | Q 17 | पृष्ठ २१

वीडियो ट्यूटोरियलVIEW ALL [1]

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 = {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.


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

(ii) R = {(xy), : xy ∈ N, x + 2y = 8}


Determine the domain and range of the relation R defined by

(i) R = [(xx + 5): x ∈ (0, 1, 2, 3, 4, 5)]


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 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.


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:
(i) (ab) R (ab) for all (ab) ∈ N × N


If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(xy) : xy ∈ A × B and x > y}


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


If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R 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 on N defined by x + 2y = 8. The domain of R is


If (x − 1, y + 4) = (1, 2) find the values of x and y


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


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

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


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

R6 = {(a, b)/a ∈ N, a < 6 and b = 4}


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

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

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


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


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


Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`


Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”


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


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

R2 = {(x, |x |) | x is a real number}


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×