Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
A = {1, 2, 3, 4} and B = {1, 5, 9, 11, 15, 16}
∴ A × B = {(1, 1), (1, 5), (1, 9), (1, 11), (1, 15), (1, 16), (2, 1), (2, 5), (2, 9), (2, 11), (2, 15), (2, 16), (3, 1), (3, 5), (3, 9), (3, 11), (3, 15), (3, 16), (4, 1), (4, 5), (4, 9), (4, 11), (4, 15), (4, 16)}
It is given that f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B.
It is observed that f is a subset of A × B.
Thus, f is a relation from A to B.
APPEARS IN
संबंधित प्रश्न
The given figure shows a relationship between the sets P and Q. Write this relation
- in set-builder form.
- in roster form.
What is its domain and range?
Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
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.
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:
(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}
Find the inverse relation R−1 in each of the cases:
(ii) R = {(x, y), : x, y ∈ N, x + 2y = 8}
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 = [(x, y) : x, y ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.
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
If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P
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}
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:
Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}
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 reflexive
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 transitive
Multiple Choice Question :
The range of the relation R = {(x, x2) | x is a prime number less than 13} is ________
Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`
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 equivalence
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
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 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
In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation
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?
Is the following relation a function? Justify your answer
R2 = {(x, |x |) | x is a real number}
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.
s = {(n, n2) | n is a positive integer}
A function from set \(A\) to set \(B\) is a relation in which:
Which condition must hold for a relation to be a function from \(A\) to \(B\)?
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 \(A\)?
For \(R=\{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)\}\) from \(A\) to \(B=\{1,4,5\}\), which statement is correct?
Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \(A\times(B\cap C)\)?
