Answer
a. No, 0 is not in ∅ since ∅ is defined as an empty set with no elements.
b. No, ∅ is an empty set with no elements and {∅} is a set containing one element that is an empty set.
c. Yes, {∅} is defined as a set containing one element that is an empty set, so ∅ ϵ {∅}.
d. No, ∅ ϵ ∅ implies that “an empty set is an element of an empty set”, which is a contradiction because ∅ is an empty set that does not contain any elements.
Work Step by Step
a. No, 0 is not in ∅ since ∅ is defined as an empty set with no elements.
b. No, ∅ is an empty set with no elements and {∅} is a set containing one element that is an empty set.
c. Yes, {∅} is defined as a set containing one element that is an empty set, so ∅ ϵ {∅}.
d. No, ∅ ϵ ∅ implies that “an empty set is an element of an empty set”, which is a contradiction because ∅ is an empty set that does not contain any elements.
