Answer
a) True
b) True
c) False
d) True
e) True
f) False
Work Step by Step
a) The set contains one element which is x. So it is true that x is an element of {x}.
b) Every set is a subset of itself so it is true.
c) The set on the right contains one element which is x. It does not contain a set as an element.
** x ∈ {x} or {x} ∈ {{x}} would be true but not {x} ∈ {x}**
d) The set on the right contains 1 element which is a set of 1 element x. So it is true. (Look at the explication on c) if not clear.
e) ∅ is a subset of every set so it is true.
f) The set {x} contains only one element which is x. It does not contain an empty set.
