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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Decide whether or not each statement is true.

  • (a) a { a , { a } }

  • (b) { a } { a , { a } }

  • (c) { a } { a , { a } }

  • (d) { { a } } { a , { a } }

  • (e) A

  • (f) 0

  • (g) { }

  • (h) { }

  • (i) { }

  • (j) { } =

  • (k)

  • (l)

(a)

To determine

Whether or not the statement ‘a{a,{a}}’ is true.

Explanation

Formula used:

xA means x is an element of set A, xA means x is not an element of set A.

Explanation:

Let A={a,{a}}

(b)

To determine

Whether or not the statement ‘{a}{a,{a}}’ is true.

(c)

To determine

Whether or not the statement ‘{a}{a,{a}}’ is true.

(d)

To determine

Whether or not the statement ‘{{a}}{a,{a}}’ is true.

(e)

To determine

Whether or not the statement ‘ϕA’ is true.

(f)

To determine

Whether or not the statement ‘0ϕ’ is true.

(g)

To determine

Whether or not the statement ‘ϕ{ϕ}’ is true.

(h)

To determine

Whether or not the statement ‘ϕ{ϕ}’ is true.

(i)

To determine

Whether or not the statement ‘{ϕ}ϕ’ is true.

(k)

To determine

Whether or not the statement ‘ϕϕ’ is true.

(l)

To determine

Whether or not the statement ‘ϕϕ’ is true.

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