Advertisements
Advertisements
प्रश्न
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine B × A
उत्तर
Since A = {1, 2, 3, 4} and B = {5, 7, 9}.
Therefore, B × A = {(5, 1), (5, 2), (5, 3), (5, 4), (7, 1), (7, 2), (7, 3), (7, 4), (9, 1), (9, 2), (9, 3), (9, 4)}
APPEARS IN
संबंधित प्रश्न
State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.
If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.
If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.
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} and R = {(a, b) : a ∈ A, b ∈ A, a divides b}. Write R explicitly.
Given A = {1, 2, 3}, B = {3, 4}, C ={4, 5, 6}, find (A × B) ∩ (B × C ).
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(i) A × (B ∩ C)
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(ii) (A × B) ∩ (A × C)
Prove that:
(i) (A ∪ B) × C = (A × C) ∪ (B × C)
(ii) (A ∩ B) × C = (A × C) ∩ (B×C)
Find the domain of the real valued function of real variable:
(iv) \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]
Find the domain and range of the real valued function:
(i) \[f\left( x \right) = \frac{ax + b}{bx - a}\]
Find the domain and range of the real valued function:
(iv) \[f\left( x \right) = \sqrt{x - 3}\]
Find the domain and range of the real valued function:
(vi) \[f\left( x \right) = \left| x - 1 \right|\]
Find the domain and range of the real valued function:
(vii) \[f\left( x \right) = - \left| x \right|\]
Find f + g, f − g, cf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{ and } \frac{f}{g}\] in :
(b) If \[f\left( x \right) = \sqrt{x - 1}\] and \[g\left( x \right) = \sqrt{x + 1}\]
Let f(x) = 2x + 5 and g(x) = x2 + x. Describe (i) f + g (ii) f − g (iii) fg (iv) f/g. Find the domain in each case.
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine A × B
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is A × B = B × A?
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is n (A × B) = n (B × A)?
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × B
Let A = {–1, 2, 3} and B = {1, 3}. Determine A × A
A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find A × (B ∩ C)
State True or False for the following statement.
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.
State True or False for the following statement.
If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}
The number of elements in the set {x ∈ R: (|x| –3)|x + 4| = 6} is equal to ______.