Advertisements
Advertisements
प्रश्न
Is the given relation a function? Give reasons for your answer.
g = `"n", 1/"n" |"n"` is a positive integer
Advertisements
उत्तर
g = `"n", 1/"n" |"n"` is a positive integer
Therefore, the element n is a positive integer and the corresponding `1/"n"` will be a unique and distinct number.
Therefore, every element in the domain has unique image.
A relation is said to be function if every element of one set has one and only one image in other set.
Hence, g is a function.
APPEARS IN
संबंधित प्रश्न
Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
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?

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}.
- Write R in roster form
- Find the domain of R
- Find the 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.
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 = {(x, y) : 3x − y = 0, where x, y ∈ 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 = {(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.
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N
If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(x, y) : x, y ∈ A × B and x > y}
If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is
Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R−1 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
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
R4 = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}
Write the relation in the Roster Form. State its domain and range
R5 = {(x, y)/x + y = 3, x, y∈ {0, 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}
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:
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.
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}
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 reflexive
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
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 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is 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 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 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?
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}
