problem archive
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If \(A = \{-1, 1\}\), find \(A \times A \times A\). -
If \(A \times B = \{(a, x), (a, y), (b, x), (b, y)\}\), Find \(A\) and \(B\). -
Let \(A = \{1, 2\}\), \(B = \{1, 2, 3, 4\}\), \(C = \{5, 6\}\) and \(D = \{5, 6, 7, 8\}\). Verify that (i) \(A \times (B \cap C) = (A \times B) \cap (... -
Let \(A = \{1, 2\}\) and \(B = \{3, 4\}\). Write \(A \times B\). How many subsets will \(A \times B\) have? List them. -
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 \(A \times B\), find \(A\) and \(B\), wh... -
The Cartesian product A × A has 9 elements among which are found (−1, 0) and (0, 1). Find the set A and the remaining elements of A × A. -
Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x, y) : y = x + 1}. (i) Depict this relation using an arrow diagram. (ii) Write d... -
The Fig 2.6 shows a relation between the sets P and Q. Write this relation (i) in set-builder form, (ii) in roster form. What is its domain and range? -
Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B. -
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... -
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 r... -
The Fig 2.7 shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) 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}. (i) Write R in roster form (ii) Find t... -
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. -
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 N be the set of natural numbers and the relation R be defined on N such that \( R = \{ (x, y) : y = 2x, x, y \in N \} \). What is the domain, codo... -
Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not? (i) \( R = \{ (2,1), (3,1)...