Advertisements
Advertisements
Question
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?
Solution
Given A = {1, 2}
B = {1, 2, 3, 4}
C = {5, 6}
D = {5, 6, 7, 8}
A × C = {1, 2} × {5, 6}
= {(1, 5) (1, 6) (2, 5) (2, 6)}
B × D = {1, 2, 3, 4} × {5, 6, 7, 8}
= {(1, 5) (1, 6) (1, 7) (1, 8) (2, 5) (2, 6) (2, 7) (2, 8) (3, 5) (3, 6) (3, 7) (3, 8) (4, 5) (4, 6) (4, 7) (4, 8)}
∴ A × C ⊂ B × D
Hence it is verified.
APPEARS IN
RELATED QUESTIONS
Find A × B, A × A and B × A :
A = B = {p, q}
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 = 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)
Multiple Choice Question :
If n(A × B) = 6 and A = {1, 3} then n(B) is ________
Multiple Choice Question :
A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A ∪ C) × B] is _______
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 ______
