Advertisements
Advertisements
प्रश्न
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(iii) A × (B ∪ C)
उत्तर
Given:
A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
(iii) A × (B ∪ C)
Now,
(B ∪ C) = {3, 4, 5, 6}
∴ A × (B ∪ 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)}
APPEARS IN
संबंधित प्रश्न
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)}.
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 = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × 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 × 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)?
If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and n[(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.
State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.
If A = {1, 2}, from the set A × A × A.
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)
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \frac{1}{x}\]
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{x - 7}\]
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \sqrt{x - 2}\]
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:
(vi) \[f\left( x \right) = \left| x - 1 \right|\]
Find the domain and range of the real valued function:
(vii) \[f\left( x \right) = - \left| x \right|\]
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 B × A
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)?
If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a ∈ A, b ∈ B, find the set of ordered pairs such that 'a' is factor of 'b' and a < b.
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × B
If P = {x : x < 3, x ∈ N}, Q = {x : x ≤ 2, x ∈ W}. Find (P ∪ Q) × (P ∩ Q), where W is the set of whole numbers.
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)}.
The number of elements in the set {x ∈ R: (|x| –3)|x + 4| = 6} is equal to ______.