Question
Download Solution PDFनिम्नलिखित में से कौन सा/से कथन सही है/हैं?
- A ∪ ϕ = A
- A ∪ A = A
- A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
- A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
किसी भी सेट A, B और C के लिए निम्नलिखित गुण सत्य हैं:
- वर्गसम नियम: A ∪ A = A
- तत्समकता का नियम: A ∪ ϕ = ϕ ∪ A = A
- वितरक नियम: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) और A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
गणना:
कथन 1 : A ∪ ϕ = A
हम जानते हैं कि कथन 1 सत्य है क्योंकि तत्समकता के नियम के अनुसार A ∪ ϕ = ϕ ∪ A = A
कथन 2: A ∪ A = A
हम जानते हैं कि कथन 2 सत्य है क्योंकि वर्गसम नियम के अनुसार A ∪ A = A
कथन 3: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
हम जानते हैं कि कथन 3 सत्य है क्योंकि वितरक नियम के अनुसार A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) and A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
कथन 4: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
हम जानते हैं कि कथन 4 सत्य है क्योंकि वितरक नियम के अनुसार A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) and A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
इसलिए, सभी कथन सत्य हैं।
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