हिंदी

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

योग
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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Sets and Relations - Exercise 5.2 [पृष्ठ १०३]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
अध्याय 5 Sets and Relations
Exercise 5.2 | Q 4 | पृष्ठ १०३

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.


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.


If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.


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

(ii) R = {(x, y), : x, y ∈ N, x + 2y = 8}


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

(iii) R is a relation from {11, 12, 13} to (8, 10, 12] defined by y = x − 3.

 

Determine the domain and range of the relation R defined by

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

 

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 = {a, b}. List all relations on A and find their number.

 

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 = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.


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


If R is a relation on a finite set having n elements, then the number of relations on A 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)


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

R3 = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}


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?

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


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 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


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 symmetric


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


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


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:

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 set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which 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


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

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


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.


Which statement defines a relation from set \(A\) to set \(B\)?


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


For a relation \(R\), the range is the set of all:


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


Given \(A=\{1,2,3,4,5\}\), which relation consists of ordered pairs satisfying \(x+y=5\), where \(x,y\in A\)?


Why is \(R=\{(1,4),(2,3),(3,2),(4,1)\}\) not a function on \(A=\{1,2,3,4,5\}\)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×