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.
Similar Questions
. 0 ∈ ∅ 2. ∅ ∈ {0} 3. {0} ⊆ ∅4. ∅ ⊂ {0} 5. {∅} ⊆ {∅} 6. {0} ⊆ {0}7. ∅ ∈ {∅} 8. {∅} ∈ {{∅}} 9. {∅} ⊂ {∅, {∅}}10. x ∈ {x} 11. ∅ ⊆ {x} 12. ∅ ∈ {x}Lec 2 TS 5
Determine the truth values of the following propositions. Explain.a) ∅ ∈ {1}b) {1} ∈ {1}c) {1} ⊂ {1}d) {1} ∈ {1, {1}}e) {1} ⊆ {1, {1}}f) {{1}} ∈ 𝒫({1, {1}})
1. {x: x is an integer neither positive nor negative} is ________a) Empty setb) Non-empty setc) Finite setd) Non- empty and Finite set
6. Which of the following statements is used to create an empty set?*4 points{ }set()[ ]( )
Which of the following statements are correct? Choose all that apply.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.