Mixing
How can I prove this statement about subsets?
Clash Royale CLAN TAG#URR8PPP
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Let $A$, $B$, $C$ be sets. Prove that if $A subseteq C$ and $B subseteq C$ then $A cup B subseteq C$.
This is an exercise in mathematical logic.
My attempt to progress forward: This statement can be written as$$
(A subseteq C) land (B subseteq C) → A cup B subseteq C\
(x in A → x in C) land (x in B → x in C) → A cup B subseteq C
$$
But I am not even sure that is how I am supposed to do it so I am a bit stuck. Can anyone explain to me how to get through this proof? Thanks in advance.
elementary-set-theory logic
edited 13 mins ago
Taroccoesbrocco
4,21461535
asked 1 hour ago
Victor Lotz
161
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Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
3
down vote
favorite
Let $A$, $B$, $C$ be sets. Prove that if $A subseteq C$ and $B subseteq C$ then $A cup B subseteq C$.
This is an exercise in mathematical logic.
My attempt to progress forward: This statement can be written as$$
(A subseteq C) land (B subseteq C) → A cup B subseteq C\
(x in A → x in C) land (x in B → x in C) → A cup B subseteq C
$$
But I am not even sure that is how I am supposed to do it so I am a bit stuck. Can anyone explain to me how to get through this proof? Thanks in advance.
elementary-set-theory logic
edited 13 mins ago
Taroccoesbrocco
4,21461535
asked 1 hour ago
Victor Lotz
161
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Let $A$, $B$, $C$ be sets. Prove that if $A subseteq C$ and $B subseteq C$ then $A cup B subseteq C$.
This is an exercise in mathematical logic.
My attempt to progress forward: This statement can be written as$$
(A subseteq C) land (B subseteq C) → A cup B subseteq C\
(x in A → x in C) land (x in B → x in C) → A cup B subseteq C
$$
But I am not even sure that is how I am supposed to do it so I am a bit stuck. Can anyone explain to me how to get through this proof? Thanks in advance.
elementary-set-theory logic
edited 13 mins ago
Taroccoesbrocco
4,21461535
asked 1 hour ago
Victor Lotz
161
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let $A$, $B$, $C$ be sets. Prove that if $A subseteq C$ and $B subseteq C$ then $A cup B subseteq C$.
This is an exercise in mathematical logic.
My attempt to progress forward: This statement can be written as$$
(A subseteq C) land (B subseteq C) → A cup B subseteq C\
(x in A → x in C) land (x in B → x in C) → A cup B subseteq C
$$
But I am not even sure that is how I am supposed to do it so I am a bit stuck. Can anyone explain to me how to get through this proof? Thanks in advance.
elementary-set-theory logic
elementary-set-theory logic
edited 13 mins ago
Taroccoesbrocco
4,21461535
asked 1 hour ago
Victor Lotz
161
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 mins ago
Taroccoesbrocco
4,21461535
asked 1 hour ago
Victor Lotz
161
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 mins ago
Taroccoesbrocco
4,21461535
edited 13 mins ago
Taroccoesbrocco
4,21461535
edited 13 mins ago
Taroccoesbrocco
4,21461535
4,21461535
asked 1 hour ago
Victor Lotz
161
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Victor Lotz
161
asked 1 hour ago
Victor Lotz
161
161
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Victor Lotz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
2 Answers
2
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oldest
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up vote
6
down vote
Take any $xin Acup B$. That means either $xin A$ or $xin B$. Anyway you get $xin C$.
answered 1 hour ago
Mark
2,482111
add a comment |Â
up vote
2
down vote
If $A subset C$, and $B subset C$;
$A cap C =A$; and $B cap C = B$;
$Acup B = (A cap C)cup (B cap C) =$
$C cap (A cup B) subset C$
answered 1 hour ago
Peter Szilas
8,5402617
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
Take any $xin Acup B$. That means either $xin A$ or $xin B$. Anyway you get $xin C$.
answered 1 hour ago
Mark
2,482111
add a comment |Â
up vote
6
down vote
Take any $xin Acup B$. That means either $xin A$ or $xin B$. Anyway you get $xin C$.
answered 1 hour ago
Mark
2,482111
add a comment |Â
up vote
6
down vote
up vote
6
down vote
Take any $xin Acup B$. That means either $xin A$ or $xin B$. Anyway you get $xin C$.
answered 1 hour ago
Mark
2,482111
Take any $xin Acup B$. That means either $xin A$ or $xin B$. Anyway you get $xin C$.
answered 1 hour ago
Mark
2,482111
answered 1 hour ago
Mark
2,482111
answered 1 hour ago
Mark
2,482111
answered 1 hour ago
Mark
2,482111
2,482111
add a comment |Â
add a comment |Â
up vote
2
down vote
If $A subset C$, and $B subset C$;
$A cap C =A$; and $B cap C = B$;
$Acup B = (A cap C)cup (B cap C) =$
$C cap (A cup B) subset C$
answered 1 hour ago
Peter Szilas
8,5402617
add a comment |Â
up vote
2
down vote
If $A subset C$, and $B subset C$;
$A cap C =A$; and $B cap C = B$;
$Acup B = (A cap C)cup (B cap C) =$
$C cap (A cup B) subset C$
answered 1 hour ago
Peter Szilas
8,5402617
add a comment |Â
up vote
2
down vote
up vote
2
down vote
If $A subset C$, and $B subset C$;
$A cap C =A$; and $B cap C = B$;
$Acup B = (A cap C)cup (B cap C) =$
$C cap (A cup B) subset C$
answered 1 hour ago
Peter Szilas
8,5402617
If $A subset C$, and $B subset C$;
$A cap C =A$; and $B cap C = B$;
$Acup B = (A cap C)cup (B cap C) =$
$C cap (A cup B) subset C$
answered 1 hour ago
Peter Szilas
8,5402617
edited 1 hour ago
answered 1 hour ago
Peter Szilas
8,5402617
answered 1 hour ago
Peter Szilas
8,5402617
answered 1 hour ago
Peter Szilas
8,5402617
8,5402617
add a comment |Â
add a comment |Â
Victor Lotz is a new contributor. Be nice, and check out our Code of Conduct.
Victor Lotz is a new contributor. Be nice, and check out our Code of Conduct.
Victor Lotz is a new contributor. Be nice, and check out our Code of Conduct.
Victor Lotz is a new contributor. Be nice, and check out our Code of Conduct.
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