Advertisements
Advertisements
प्रश्न
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(i) A × (B ∩ C)
उत्तर
Given:
A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
(i) A × (B ∩ C)
Now,
(B ∩ C) = {4}
∴ A × (B ∩ C) = {(1, 4), (2, 4), (3, 4)}
APPEARS IN
संबंधित प्रश्न
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B).
If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
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 = {–1, 1}, find A × A × A.
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)
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, find A and B, where x, y and z are distinct elements.
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.
If A = {1, 2, 3} and B = {2, 4}, what are A × B, B × A, A × A, B × B and (A × B) ∩ (B × A)?
Let A and B be two sets. Show that the sets A × B and B × A have elements in common iff the sets A and B have an elements in common.
If A = {−1, 1}, find A × A × A.
If A = {2, 3}, B = {4, 5}, C ={5, 6}, find A × (B ∪ C), A × (B ∩ C), (A × B) ∪ (A × C).
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:
(i) A × C ⊂ B × D
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(iii) A × (B ∪ C)
Prove that:
(i) (A ∪ B) × C = (A × C) ∪ (B × C)
(ii) (A ∩ B) × C = (A × C) ∩ (B×C)
If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.
Find the domain of the real valued function of real variable:
(v) \[f\left( x \right) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}\]
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]
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:
(iv) \[f\left( x \right) = \sqrt{x - 3}\]
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 :
(a) If f(x) = x3 + 1 and g(x) = x + 1
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 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 A × B
A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find A × (B ∩ C)