{∅} ⊆ {x} Is this true (can also be written as {{ }} ⊆ {x}}
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Is {∅} ⊆ {x} true or false?
I'm guessing it is false as empty-set within the set is not within the x set.
If it was ∅ ⊆ {x} then it would be true.
Is this right?
elementary-set-theory
asked Nov 15 at 16:41
anon2000
32
add a comment |
up vote
0
down vote
favorite
Is {∅} ⊆ {x} true or false?
I'm guessing it is false as empty-set within the set is not within the x set.
If it was ∅ ⊆ {x} then it would be true.
Is this right?
elementary-set-theory
asked Nov 15 at 16:41
anon2000
32
If $xneqemptyset$ then $emptysetnotin{x}$, so ${emptyset}notsubseteq{x}$.
– SmileyCraft
Nov 15 at 16:44
Well, what is $x$?
– user76284
Nov 15 at 16:46
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is {∅} ⊆ {x} true or false?
I'm guessing it is false as empty-set within the set is not within the x set.
If it was ∅ ⊆ {x} then it would be true.
Is this right?
elementary-set-theory
asked Nov 15 at 16:41
anon2000
32
Is {∅} ⊆ {x} true or false?
I'm guessing it is false as empty-set within the set is not within the x set.
If it was ∅ ⊆ {x} then it would be true.
Is this right?
elementary-set-theory
elementary-set-theory
asked Nov 15 at 16:41
anon2000
32
asked Nov 15 at 16:41
anon2000
32
asked Nov 15 at 16:41
anon2000
32
asked Nov 15 at 16:41
anon2000
32
asked Nov 15 at 16:41
anon2000
32
32
If $xneqemptyset$ then $emptysetnotin{x}$, so ${emptyset}notsubseteq{x}$.
– SmileyCraft
Nov 15 at 16:44
Well, what is $x$?
– user76284
Nov 15 at 16:46
add a comment |
If $xneqemptyset$ then $emptysetnotin{x}$, so ${emptyset}notsubseteq{x}$.
– SmileyCraft
Nov 15 at 16:44
Well, what is $x$?
– user76284
Nov 15 at 16:46
If $xneqemptyset$ then $emptysetnotin{x}$, so ${emptyset}notsubseteq{x}$.
– SmileyCraft
Nov 15 at 16:44
If $xneqemptyset$ then $emptysetnotin{x}$, so ${emptyset}notsubseteq{x}$.
– SmileyCraft
Nov 15 at 16:44
Well, what is $x$?
– user76284
Nov 15 at 16:46
Well, what is $x$?
– user76284
Nov 15 at 16:46
add a comment |
2 Answers
2
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0
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accepted
Yes, you are right. As $varnothing in {varnothing}$ but $varnothing notin {x}$ (assuming $x$ is non-empty), we have ${varnothing}notsubseteq {x}$.
We also do have $varnothing subseteq {x}$, because there is no element $yin varnothing$ which can serve as a witness that it is false.
answered Nov 15 at 16:45
Arthur
108k7103186
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If $x=emptyset$, then ${emptyset}subseteq{x}$ is true. If $xneemptyset$, then it is false. On the other hand, $emptysetsubseteq A$ is true for any set $A$.
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Yes, you are right. As $varnothing in {varnothing}$ but $varnothing notin {x}$ (assuming $x$ is non-empty), we have ${varnothing}notsubseteq {x}$.
We also do have $varnothing subseteq {x}$, because there is no element $yin varnothing$ which can serve as a witness that it is false.
answered Nov 15 at 16:45
Arthur
108k7103186
add a comment |
up vote
0
down vote
accepted
Yes, you are right. As $varnothing in {varnothing}$ but $varnothing notin {x}$ (assuming $x$ is non-empty), we have ${varnothing}notsubseteq {x}$.
We also do have $varnothing subseteq {x}$, because there is no element $yin varnothing$ which can serve as a witness that it is false.
answered Nov 15 at 16:45
Arthur
108k7103186
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Yes, you are right. As $varnothing in {varnothing}$ but $varnothing notin {x}$ (assuming $x$ is non-empty), we have ${varnothing}notsubseteq {x}$.
We also do have $varnothing subseteq {x}$, because there is no element $yin varnothing$ which can serve as a witness that it is false.
answered Nov 15 at 16:45
Arthur
108k7103186
Yes, you are right. As $varnothing in {varnothing}$ but $varnothing notin {x}$ (assuming $x$ is non-empty), we have ${varnothing}notsubseteq {x}$.
We also do have $varnothing subseteq {x}$, because there is no element $yin varnothing$ which can serve as a witness that it is false.
answered Nov 15 at 16:45
Arthur
108k7103186
answered Nov 15 at 16:45
Arthur
108k7103186
answered Nov 15 at 16:45
Arthur
108k7103186
answered Nov 15 at 16:45
Arthur
108k7103186
108k7103186
add a comment |
add a comment |
up vote
0
down vote
If $x=emptyset$, then ${emptyset}subseteq{x}$ is true. If $xneemptyset$, then it is false. On the other hand, $emptysetsubseteq A$ is true for any set $A$.
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
add a comment |
up vote
0
down vote
If $x=emptyset$, then ${emptyset}subseteq{x}$ is true. If $xneemptyset$, then it is false. On the other hand, $emptysetsubseteq A$ is true for any set $A$.
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
add a comment |
up vote
0
down vote
up vote
0
down vote
If $x=emptyset$, then ${emptyset}subseteq{x}$ is true. If $xneemptyset$, then it is false. On the other hand, $emptysetsubseteq A$ is true for any set $A$.
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
If $x=emptyset$, then ${emptyset}subseteq{x}$ is true. If $xneemptyset$, then it is false. On the other hand, $emptysetsubseteq A$ is true for any set $A$.
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
answered Nov 15 at 16:45
Saucy O'Path
5,5811425
5,5811425
add a comment |
add a comment |
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If $xneqemptyset$ then $emptysetnotin{x}$, so ${emptyset}notsubseteq{x}$.
– SmileyCraft
Nov 15 at 16:44
Well, what is $x$?
– user76284
Nov 15 at 16:46