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Chapter 2: Q. 2.3 (page 52)

F=FE∪FEcandE∪F=E∪EcF

Short Answer

Expert verified

Use associative and distributive laws.

F=FE∪FEcandE∪F=E∪EcF

Step by step solution

01

Given Information.

F=FE∪FEcandE∪F=E∪EcF

02

Explanation.

F=FE∪FEcandE∪F=E∪EcFF=F∩SA⊆B⇒A∩B=A(from def. of intersection)=F∩E∪EcS=E∪Ec(from def. of complement)=FE∪FEcdistributive law

This proves:

F=FE∪FEc

E∪F=E∪FE∪FEcby previously proven identity

=(E∪FE)∪FEc associative law

role="math" localid="1649044670063" =E∪FEcA⊆B⇒A∪B=B(from def. of the union)

This proves:

E∪F=E∪FEc

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