Solution to (i) Determine whether each of these statements is true or false. (a) 0∈∅ (b)∅∈{0} (c){0}⊂∅ … - Sikademy
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Archangel Macsika

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

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Here's the Solution to this Question

1)

a)0 \in\varnothing

Ans : False

Empty set does not contain any elements

b)\varnothing \isin {0}

Empty set is an element of set that contains only zero

So answer is false

c)

{0}\subset \varnothing

The empty set that contains nothing so set zero is not the subset of empty set

d)\varnothing\subset {0}

The set zero contains empty set so empty set is subset of zero set

Answer is true

e){0}\isin {0}


The set containing zero element so zero elements belongs to set of zero not zero set{0}

So answer is false

F){0}\subset {0}

A set is always not a subset of itself ,because the sets are completely identical

Given statment is false

G){0} subset {0}

Set is subset of itself

Answer is true

2)

a)\varnothing\isin {\varnothing }

The empty set contains empty, so empty strings belongs to empty set

So true

b)

\varnothing\isin {\varnothing ,{\varnothing }}

The empty elements belongs to set and subset of empty

So answer is true

c){\varnothing }\isin {\varnothing }

The set containing elements, not containing sets

So answer is false

d){\varnothing }\isin {{\varnothing }}

The empty set is an element of set

So answer is true

e){ \varnothing}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So true

f){{\varnothing }}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So answer is true

G){{\varnothing }}\subset {{\varnothing} ,{\varnothing}}

Answer is false

Proper set not equal sets

1)

a)0 \in\varnothing

Ans : False

Empty set does not contain any elements

b)\varnothing \isin {0}

Empty set is an element of set that contains only zero

So answer is false

c)

{0}\subset \varnothing

The empty set that contains nothing so set zero is not the subset of empty set

d)\varnothing\subset {0}

The set zero contains empty set so empty set is subset of zero set

Answer is true

e){0}\isin {0}


The set containing zero element so zero elements belongs to set of zero not zero set{0}

So answer is false

F){0}\subset {0}

A set is always not a subset of itself ,because the sets are completely identical

Given statment is false

G){0} subset {0}

Set is subset of itself

Answer is true

2)

a)\varnothing\isin {\varnothing }

The empty set contains empty, so empty strings belongs to empty set

So true

b)

\varnothing\isin {\varnothing ,{\varnothing }}

The empty elements belongs to set and subset of empty

So answer is true

c){\varnothing }\isin {\varnothing }

The set containing elements, not containing sets

So answer is false

d){\varnothing }\isin {{\varnothing }}

The empty set is an element of set

So answer is true

e){ \varnothing}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So true

f){{\varnothing }}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So answer is true

G){{\varnothing }}\subset {{\varnothing} ,{\varnothing}}

Answer is false

Proper set not equal sets

1)

a)0 \in\varnothing

Ans : False

Empty set does not contain any elements

b)\varnothing \isin {0}

Empty set is an element of set that contains only zero

So answer is false

c)

{0}\subset \varnothing

The empty set that contains nothing so set zero is not the subset of empty set

d)\varnothing\subset {0}

The set zero contains empty set so empty set is subset of zero set

Answer is true

e){0}\isin {0}


The set containing zero element so zero elements belongs to set of zero not zero set{0}

So answer is false

F){0}\subset {0}

A set is always not a subset of itself ,because the sets are completely identical

Given statment is false

G){0} subset {0}

Set is subset of itself

Answer is true

2)

a)\varnothing\isin {\varnothing }

The empty set contains empty, so empty strings belongs to empty set

So true

b)

\varnothing\isin {\varnothing ,{\varnothing }}

The empty elements belongs to set and subset of empty

So answer is true

c){\varnothing }\isin {\varnothing }

The set containing elements, not containing sets

So answer is false

d){\varnothing }\isin {{\varnothing }}

The empty set is an element of set

So answer is true

e){ \varnothing}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So true

f){{\varnothing }}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So answer is true

G){{\varnothing }}\subset {{\varnothing} ,{\varnothing}}

Answer is false

Proper set not equal sets

1)

a)0 \in\varnothing

Ans : False

Empty set does not contain any elements

b)\varnothing \isin {0}

Empty set is an element of set that contains only zero

So answer is false

c)

{0}\subset \varnothing

The empty set that contains nothing so set zero is not the subset of empty set

d)\varnothing\subset {0}

The set zero contains empty set so empty set is subset of zero set

Answer is true

e){0}\isin {0}


The set containing zero element so zero elements belongs to set of zero not zero set{0}

So answer is false

F){0}\subset {0}

A set is always not a subset of itself ,because the sets are completely identical

Given statment is false

G){0} subset {0}

Set is subset of itself

Answer is true

2)

a)\varnothing\isin {\varnothing }

The empty set contains empty, so empty strings belongs to empty set

So true

b)

\varnothing\isin {\varnothing ,{\varnothing }}

The empty elements belongs to set and subset of empty

So answer is true

c){\varnothing }\isin {\varnothing }

The set containing elements, not containing sets

So answer is false

d){\varnothing }\isin {{\varnothing }}

The empty set is an element of set

So answer is true

e){ \varnothing}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So true

f){{\varnothing }}\subset {\varnothing ,{\varnothing }}

The empty string is subset of given set

So answer is true

G){{\varnothing }}\subset {{\varnothing} ,{\varnothing}}

Answer is false

Proper set not equal sets


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Question ID: mtid-5-stid-8-sqid-3867-qpid-2566