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.
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