Question
Download Solution PDFA మరియు B రెండు సమితులైతే A ∩ (B ∪ A)c కు సమానమైనది
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFభావన:
డీ మార్గాన్ నియమం:
(A ∪ B)c = Ac ∩ Bc
(A ∩ B)c = Ac ∪ Bc
సమితులలో విభాజక నియమం:
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
గణన:
ఇవ్వబడింది: A మరియు B రెండు సమితులు
కనుగొనవలసినది: A ∩ (B ∪ A)c
(A ∪ B)c = Ac ∩ Bc అని మనకు తెలుసు
కాబట్టి (B ∪ A)c = Bc ∩ Ac
ఇప్పుడు A ∩ (B ∪ A)c = A ∩ (Bc ∩ Ac)
= (A ∩ Bc) ∩ (A ∩ Ac) (విభాజక నియమాన్ని ఉపయోగించి)
= (A ∩ Bc) ∩ ϕ (∵ x ∩ ϕ = ϕ)
= ϕ
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