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 Set Theory (Posted on 2014-04-19)

The following is a list of 15 thought provoking statements
A denotes any set, F the set {1,2}, φ the empty set,
and ℘(S) the set of all subsets of set S (i.e, the power
set of S).

a)   φ∩{φ} = {φ}
b)   φ∪{φ} = {φ,{φ}}
c)   φ ∈ ℘({φ,{φ}})
d)   {φ} ⊆ A
e)   φ ⊆ A
f)   φ ⊆ ℘(A)
g)   {{φ}} ⊆ ℘(φ)
h)   {φ}∩φ = φ
i)   ℘(φ) = {φ,{φ}}
j)   φ ∈ A
k)   φ ∈ ℘(A)
l)   {φ} ∈ ℘(A)
m)   {φ}∪φ = {φ}
n)   φ ⊆ ℘(F)-φ
o)   {φ} ⊆ {{φ,{φ},{{φ}}}}

From "Bridge to Abstract Mathematics",1987
by Ronald P. Morash.

 Submitted by Bractals No Rating Solution: (Hide) A denotes any set, F the set {1,2}, φ the empty set, and ℘(S) the set of all subsets of set S (i.e, the power set of S).To reduce the number of {} we will denote {φ} by θ``` STATEMENT (T/F) REASON --------- ----- ------ a) φ∩θ = θ F φ∩θ = φ ≠ θ b) φ∪θ = {φ,θ} F φ∪θ = θ ≠ {φ,θ} c) φ ∈ ℘({φ,θ}) T φ ∈ ℘(A) ∀A d) θ ⊆ A F θ ⊄ A for A = φ e) φ ⊆ A T φ ⊆ A ∀A f) φ ⊆ ℘(A) T φ ⊆ A ∀A g) {θ} ⊆ ℘(φ) F {θ} ⊄ ℘(φ) ℘(φ) = θ h) θ∩φ = φ T θ∩φ = φ i) ℘(φ) = {φ,θ} F ℘(φ) = θ ≠ {φ,θ} j) φ ∈ A F φ ∉ φ for A = φ k) φ ∈ ℘(A) T φ ∈ ℘(A) ∀A l) θ ∈ ℘(A) F θ ∉ θ for A = φ m) θ∪φ = θ T θ∪φ = θ n) φ ⊆ ℘(F)-φ T φ ⊆ A ∀A o) θ ⊆ {{φ,θ,{θ}}} F φ ≠ {φ,θ,{θ}}``` These are my answers and only a few from "Bridge to Abstract Mathematics",1987  by Ronald P. Morash.

 Subject Author Date re: attempt at the rest Charlie 2014-04-19 14:49:15 attempt at the rest Charlie 2014-04-19 11:01:51 right off the bat Charlie 2014-04-19 09:39:42

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