Advertisements
Advertisements
Question
Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∩ C) = (A × B) ∩ (A × C)
Advertisements
Solution
A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}
B ∩ C = {5, 6}
∴ A × (B ∩ C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}
A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}
A × C = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}
∴ (A × B) ∩ (A × C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}
∴ A × (B ∩ C) = (A × B) ∩ (A × C)
APPEARS IN
RELATED QUESTIONS
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.
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.
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.
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:
(iii) R is a relation from {11, 12, 13} to (8, 10, 12] defined by y = x − 3.
Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.
Determine the domain and range of the relations:
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
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.
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 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 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.
A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is
If (x − 1, y + 4) = (1, 2) find the values of x and y
If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P
Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)
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:
Determine the domain and range of the following relation.
R = {(a, b)/a ∈ N, a < 5, b = 4}
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 is set of all books. given by R = {(x, y)/x and y have same number of pages}
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R4 = {(7, –1), (0, 3), (3, 3), (0, 7)}
Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R
Multiple Choice Question :
The range of the relation R = {(x, x2) | x is a prime number less than 13} is ________
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 ________.
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 reflexive
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
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:
The number of relations on a set containing 3 elements is
Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.
Is the given relation a function? Give reasons for your answer.
g = `"n", 1/"n" |"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 ______.
