Which of the following statements are true about the sets. A. 0 ∈ ∅ B. ∅ ∈ {0}…

Final answer: The true statements are ∅ ∈ {∅} and {∅} ⊂ {∅, {∅}}.

• 0 ∈ ∅ — False. The empty set has no elements, so no object (including 0) is an element of it.

• ∅ ∈ {0} — False. The set {0} contains only the element 0; the empty set is not that element.

• ∅ ∈ {∅} — True. The set {∅} has exactly one element, which is the empty set itself.

• {∅} ∈ {∅} — False. The element of {∅} is ∅; the set {∅} is not an element of {∅} (that would require a nested occurrence: {{∅}}).

• {∅} ⊂ {∅, {∅}} — True. Every element of {∅} (namely ∅) is in the larger set, and the larger set has an additional element ({∅}), so the inclusion is proper.

Key distinction: Being an element (∈) is different from being a subset (⊂). For example, ∅ ∈ {∅} is true while {∅} ⊂ {∅, {∅}} is a statement about subset inclusion.