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

If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P

Advertisements
Advertisements

प्रश्न

If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P

बेरीज
Advertisements

उत्तर

P = {1, 2, 3), Q = {1, 4}

∴ P × Q = {(1, 1), (1, 4), (2, 1), (2, 4), (3, 1), (3, 4)}

and Q × P = {(1, 1), (1, 2), (1, 3), (4, 1), (4, 2), (4, 3)}.

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

APPEARS IN

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 R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.


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.


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

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}


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

 

Determine the domain and range of the relation R defined by

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


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


If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x2 + y2 = 9, then write domain of R.


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


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 = {6, 8} and B = {1, 3, 5}
Show that R1 = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R2 = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation


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.

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

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


Answer the following:

Determine the domain and range of the following relation.

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


Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}


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, 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


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 ________.


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


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


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 equivalence


Choose the correct alternative:

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


Is the following relation a function? Justify your answer

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


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.


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

h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}


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 ______.


Which condition must hold for a relation to be a function from \(A\) to \(B\)?


Which statement about images in a function is correct?


When are two ordered pairs \((a,b)\) and \((c,d)\) equal?


The Cartesian product \(A\times A\) has \(9\) elements and contains \((-1,0)\) and \((0,1)\). What is \(A\)?


Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \((A\times B)\cap(A\times C)\)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×