Advertisements
Advertisements
Question
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.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
Since (2, 9), (2, 11) f i.e., f contains two ordered pairs with the same first element. Hence, f is not a function from A to B.
APPEARS IN
RELATED QUESTIONS
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}}.
Write the relation R = {(x, x3): x is a prime number less than 10} 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:
(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}
The adjacent figure shows a relationship between the sets P and Q. Write this relation in (i) set builder form (ii) roster form. What is its domain and range?
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.
Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B
Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(x, y) : x − yis odd}. Write R in roster form.
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)
Express {(x, y) / x2 + y2 = 100, where x, y ∈ W} as a set of ordered pairs
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
R7 = {(a, b)/a, b ∈ N, a + b = 6}
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:
Show that the following is an equivalence relation
R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}
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 ________.
Discuss the following relation for reflexivity, symmetricity and transitivity:
The relation R defined on the set of all positive integers by “mRn if m divides n”
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the female members of a family. The relation R defined by “aRb if a is not a sister of b”
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 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
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 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 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 symmetric
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 R2 = {(x, y) | x and y are integers and x2 + y2 = 64} is a relation. Then find R2.
Is the given relation a function? Give reasons for your answer.
f = {(x, x) | x is a real number}
Is the given relation a function? Give reasons for your answer.
g = `"n", 1/"n" |"n"` is a positive integer
Is the given relation a function? Give reasons for your answer.
s = {(n, n2) | n is a positive integer}
Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.
Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.
