Question

Determine whether these statements are true or false.

a.∅ ∈ {∅}
b.∅ ∈ {∅,{∅}}
c.{∅} ∈ {∅}
d.{∅} ∈ {{∅}}
e.{∅} ⊂ {∅,{∅}} f ) {{∅}} ⊂ {∅,{∅}} g) {{∅}} ⊂ {{∅},{∅}}

Answer 1

a. True
b. True
c. False; a set can't belong to itself
d. True
e. True
f. False; the only subsets of
`\{\varnothing,\{\varnothing\}\}` are
`\varnothing`,
`\{\varnothing\}`, and
`\{\varnothing,\{\varnothing\}\}`
g. True