Advertisements
Advertisements
प्रश्न
If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).
Advertisements
उत्तर
Given:
A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}
Now,
(A − C) = {1, 4}
(B − C) = {4}
Thus, we have:
(A − C) × (B − C) = {(1, 4), (4, 4)}
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.
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 = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.
Determine the domain and range of the relation R defined by
(ii) R = {(x, x3) : x is a prime number less than 10}
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
(iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ∈ N × N
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.
If R is a relation from set A = (11, 12, 13) to set B = (8, 10, 12) defined by y = x − 3, then write R−1.
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 R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.
If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then 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
A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 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
Write the relation in the Roster Form. State its domain and range
R1 = {(a, a2)/a is prime number less than 15}
Identify which of if the following relations are reflexive, symmetric, and transitive.
| Relation | Reflexive | Symmetric | Transitive |
| R = {(a, b) : a, b ∈ Z, a – b is an integer} | |||
| R = {(a, b) : a, b ∈ N, a + b is even} | √ | √ | x |
| R = {(a, b) : a, b ∈ N, a divides b} | |||
| R = {(a, b) : a, b ∈ N, a2 – 4ab + 3b2 = 0} | |||
| R = {(a, b) : a is sister of b and a, b ∈ G = Set of girls} | |||
| R = {(a, b) : Line a is perpendicular to line b in a plane} | |||
| R = {(a, b) : a, b ∈ R, a < b} | |||
| R = {(a, b) : a, b ∈ R, a ≤ b3} |
Select the correct answer from given alternative.
The relation ">" in the set of N (Natural number) is
Select the correct answer from given alternative.
A relation between A and B is
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:
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 symmentric
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}
Multiple Choice Question :
If there are 1024 relation from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in 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”
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 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 symmetric
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 transitive
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 X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is
Choose the correct alternative:
Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is
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
Which statement violates the condition for a function?
Which statement about images in a function is correct?
Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \(A\times(B\cap C)\)?
Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \((A\times B)\cap(A\times C)\)?
Why is \(R=\{(1,4),(2,3),(3,2),(4,1)\}\) not a function on \(A=\{1,2,3,4,5\}\)?
