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Gaurav Seth 5 years, 3 months ago
Important formulas :
A ∪ B = B ∪ A
A ∪ (B ∪ C) = (A ∪ B) ∪ C.
Let A and B have x elements in common .
n { (A ∩ B) × (B ∪ A) } = n { (A × B) ∩ (B × A)
⇒ n { (A ∩ B) × (B ∪ A) } = n { (A ∩ B) } × n{ (A ∩ B) }
⇒ n { (A ∩ B) × (B ∪ A) } = k × k ⇒ k²
Hence A × B and B × A have an element in common . The number of elements is k² provided that k is the number of elements in common in A and B .
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