Answer
a) False
b) False
c) False
d) True
e) False
f) False
g) True
Work Step by Step
a) 0 is a number, it is not an element of an empty set. The empty set has nothing as element.
b) ∅ means empty set. The set on the right is a set containing 1 element which is 0. It does not contain an empty set.
c) ∅ is an empty set, it does not have any element. The set {0} can't be a proper subset of an empty set.
d) It is true, because ∅ is always a subset of every set and in the set on the right side {0}, it has an element that the left set doesn't have which is the element 0. So ∅ is a proper subset of {0}.
e) The set on the side contains only 1 element which is the number 0. It doesn't contain a set which has a 0 as an element. ** 0 ∈ {0} or {0} ∈ {{0}}would be true but not {0} ∈ {0}**
f) The two sets are equal and for a set to be a proper subset of another one, they can't be equal.
g) Every set is a subset of itself. So it is true.
