Determine whether each of these statements is true or false.a) 0 ∈ ∅b) ∅ ∈ {0}c) {0} ⊂ ∅d) ∅ ⊂ {0}e) {0} ∈ {0}f) {0} ⊂ {0}g) {∅} ⊆ {∅}
Question
Determine whether each of these statements is true or false.a) 0 ∈ ∅b) ∅ ∈ {0}c) {0} ⊂ ∅d) ∅ ⊂ {0}e) {0} ∈ {0}f) {0} ⊂ {0}g) {∅} ⊆ {∅}
Solution
a) False. The empty set ∅ does not contain any elements, including 0.
b) False. The set {0} contains the element 0, not the empty set ∅.
c) False. The set {0} cannot be a subset of ∅ because ∅ does not contain any elements.
d) True. The empty set ∅ is a subset of any set, including {0}.
e) False. The set {0} is not an element of the set {0}. The set {0} contains the element 0, not the set {0}.
f) True. A set is a subset of itself, so {0} is a subset of {0}.
g) True. The set {∅} is a subset of itself.
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