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Chapter 2: Q. 2.1 (page 52)

Prove the following relations:

EF鈯�E鈯�E鈭�F

Short Answer

Expert verified

Use the definition of a subset and logical operationsEF鈯�E鈯�E鈭�F.

Step by step solution

01

Given Information.

EF鈯�E鈯�E鈭�F

02

Explanation.

EF鈯�E鈯�E鈭�F

IfEF=鈭�, then EF=鈭�is a subset of all sets by convention.

Ifx鈭�EF

By the definition of intersectionx鈭�Eandx鈭�F鈫�x鈭�E

xis a member of Eand by the definition of a subset

A鈯�B鈬�defx鈭�A鈫�x鈭�B

EF鈯�EThe same procedure for E鈯�E鈭�FIfE=鈭�then Eis a subset of all sets by convention.

Ifx鈭�E

鈫�x鈭�Eorx鈭�F

By the definition of a unionx鈭�E鈭�F

By the definitionlocalid="1649042050551" (1),E鈯�E鈭�F

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