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International Baccalaureatte | Further Maths HL
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Need help for this question! Related to set identities.
Date Posted: 2 years ago
Views: 2015
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done
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clear
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possibly mistake in question phrasing.
question says "... sets A,B and C ..."???
unless I am mistaken, when C is written as superscript, it should represent the symbol for "complement of set" (equivalent to using single quotation mark).
question says "... sets A,B and C ..."???
unless I am mistaken, when C is written as superscript, it should represent the symbol for "complement of set" (equivalent to using single quotation mark).
Date Posted:
2 years ago
alternative solution in other direction (with similar reasoning) ...
LHS
= (AUB) ∩ (A∩B)'
= (AUB) ∩ (A'UB')
= (A∩A') U (A∩B') U (B∩A') U (B∩B')
= ∅ U (A∩B') U (B∩A') U ∅
= (A∩B') U (B∩A')
= (A\B) U (B\A)
= RHS
LHS
= (AUB) ∩ (A∩B)'
= (AUB) ∩ (A'UB')
= (A∩A') U (A∩B') U (B∩A') U (B∩B')
= ∅ U (A∩B') U (B∩A') U ∅
= (A∩B') U (B∩A')
= (A\B) U (B\A)
= RHS
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