Advertisements
Advertisements
प्रश्न
Multiple Choice Question :
If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true ______
विकल्प
(A × C) ⊂ (B × D)
(B × D) ⊂ (A × C)
(A × B) ⊂ (A × D)
(D × A) ⊂ (B × A)
उत्तर
(A × C) ⊂ (B × D)
Explanation;
Hint: n(A × B) = 2 × 4 = 8
(A × C) = 2 × 2 = 4
n(B × C) = 4 × 2 = 8
n(C × D) = 2 × 4 = 8
n(A × C) = 2 × 2 = 4
n(A × D) = 2 × 4 = 8
n(B × D) = 4 × 4 = 16
∴ (A × C) ⊂ (B × D)
APPEARS IN
संबंधित प्रश्न
Find A × B, A × A and B × A:
A = {m, n}; B = Φ
If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, Show that A × A = (B × B) ∩ (C × C)
Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if (A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D) is true?
Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that A × (B ∪ C) = (A × B) ∪ (A × C)
Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)
Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that (A ∪ B) × C = (A × C) ∪ (B × C)
Let A = The set of all natural number less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that (A ∩ B) × C = (A × C) ∩ (B × C)
Let A = The set of all natural number less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that A × (B – C) = (A × B) – (A × C)
The Cartesian product A × A has 9 elements among which (– 1, 0) and (0, 1) are found. Find the set A and the remaining elements of A × A
Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify whether A × C is a subset of B × D?
