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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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In Exercise 14-35, prove each statement.

A ( B A ) =

To determine

To prove: A(BA)=ϕ

Explanation

Formula used:

1) Intersection:

If A and B are sets, the intersection of A and B is the set AB ( read as‘ A intersection B ’) given by, AB={x|xAandxB}

2) Complement:

For arbitrary subsets A and B of the universal set U, the complement of B in A is AB={xU|xAandxB}

Proof:

Use definition of complement,

BA={xU|xBandxA}

By using definition of intersection,

A(BA)={xA}

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