The following is a list of 15 thought provoking statements
about sets where a true or false answer is needed.
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.
  

I remember that the null set is a subset of every set, so right off the bat:

e, f, and n are true.

"Of course I'm doing nothing: besides everything else that I'm doing, I'm also doing nothing."

Posted by Charlie on 2014-04-19 09:39:42