Determine whether these statements are true or false. a) ∅ ∈ {∅} b) ∅ ∈ {∅,{∅}} c) {∅} ∈ {∅} d) {∅} ∈ {{∅}} e) {∅} ⊂ {∅,{∅}} f) {{∅}} ⊂ {∅,{∅}} g) {{∅}} ⊂ {{∅},{∅}}

Question

Ben

Mathematics

14 June, 00:16

Determine whether these statements are true or false. a) ∅ ∈ {∅} b) ∅ ∈ {∅,{∅}} c) {∅} ∈ {∅} d) {∅} ∈ {{∅}} e) {∅} ⊂ {∅,{∅}} f) {{∅}} ⊂ {∅,{∅}} g) {{∅}} ⊂ {{∅},{∅}}

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Ronin Ortega · Answer 1

a) ∅ ∈ {∅} TRUE

b) ∅ ∈ {∅,{∅}} TRUE

c) {∅} ∈ {∅} FALSE

d) {∅} ∈ {{∅}} TRUE

e) {∅} ⊂ {∅,{∅}} TRUE

f) {{∅}} ⊂ {∅,{∅}} TRUE

g) {{∅}} ⊂ {{∅},{∅}}FALSE

Step-by-step explanation:

To assess whether these statements are true or false, first observe the symbol:

"∈" means that element, as it is and as it is, belongs to the set. To belong to the set it must be within the symbols "{}"

On the other hand, the symbol "⊂" means "subset", that is, it is a subset that is included in the main set.

So:

c) is false because "{∅}" is not included in the set

g) is false because " {{∅}}" is not included in the set