   Chapter 1.1, Problem 3E

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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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