Boolean algebra and closure axiom
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A Boolean algebra is an algebraic system (B,$∨$,$∧$,$¬$), where $∨$ and $∧$ are binary, and $¬$ is a unary operation.
One of the Boolean algebra axiom is: If $a$ and $b$ are elements of $B$, then $(a ∨ b)$ and $(a ∧ b)$ are in $B$.
i.e. the set $B = (1111,0011,0110,1010,0000,1100,1001,0101)$ I can't use as carrier for Boolean algebra, because the result of operation $0011 ∨ 0110 = 0111$ is't in set $B$.
Is it correct? Do I correctly think about closure for $∨$ and $∧$ operators?
boolean-algebra
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
$endgroup$
add a comment |
$begingroup$
A Boolean algebra is an algebraic system (B,$∨$,$∧$,$¬$), where $∨$ and $∧$ are binary, and $¬$ is a unary operation.
One of the Boolean algebra axiom is: If $a$ and $b$ are elements of $B$, then $(a ∨ b)$ and $(a ∧ b)$ are in $B$.
i.e. the set $B = (1111,0011,0110,1010,0000,1100,1001,0101)$ I can't use as carrier for Boolean algebra, because the result of operation $0011 ∨ 0110 = 0111$ is't in set $B$.
Is it correct? Do I correctly think about closure for $∨$ and $∧$ operators?
boolean-algebra
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
$endgroup$
1
$begingroup$
Yes, that's right.
$endgroup$
– Robert Israel
Dec 20 '18 at 12:54
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@MauroALLEGRANZA because I need binary vectors.
$endgroup$
– V. Gai
Dec 20 '18 at 12:56
$begingroup$
@RobertIsrael may be you can send me link to book which explains how can I prove, that some set with operations, defined on it, is Boolean algebra?
$endgroup$
– V. Gai
Dec 20 '18 at 12:58
add a comment |
$begingroup$
A Boolean algebra is an algebraic system (B,$∨$,$∧$,$¬$), where $∨$ and $∧$ are binary, and $¬$ is a unary operation.
One of the Boolean algebra axiom is: If $a$ and $b$ are elements of $B$, then $(a ∨ b)$ and $(a ∧ b)$ are in $B$.
i.e. the set $B = (1111,0011,0110,1010,0000,1100,1001,0101)$ I can't use as carrier for Boolean algebra, because the result of operation $0011 ∨ 0110 = 0111$ is't in set $B$.
Is it correct? Do I correctly think about closure for $∨$ and $∧$ operators?
boolean-algebra
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
$endgroup$
A Boolean algebra is an algebraic system (B,$∨$,$∧$,$¬$), where $∨$ and $∧$ are binary, and $¬$ is a unary operation.
One of the Boolean algebra axiom is: If $a$ and $b$ are elements of $B$, then $(a ∨ b)$ and $(a ∧ b)$ are in $B$.
i.e. the set $B = (1111,0011,0110,1010,0000,1100,1001,0101)$ I can't use as carrier for Boolean algebra, because the result of operation $0011 ∨ 0110 = 0111$ is't in set $B$.
Is it correct? Do I correctly think about closure for $∨$ and $∧$ operators?
boolean-algebra
boolean-algebra
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
asked Dec 20 '18 at 12:51
V. GaiV. Gai
62
62
1
$begingroup$
Yes, that's right.
$endgroup$
– Robert Israel
Dec 20 '18 at 12:54
$begingroup$
@MauroALLEGRANZA because I need binary vectors.
$endgroup$
– V. Gai
Dec 20 '18 at 12:56
$begingroup$
@RobertIsrael may be you can send me link to book which explains how can I prove, that some set with operations, defined on it, is Boolean algebra?
$endgroup$
– V. Gai
Dec 20 '18 at 12:58
add a comment |
1
$begingroup$
Yes, that's right.
$endgroup$
– Robert Israel
Dec 20 '18 at 12:54
$begingroup$
@MauroALLEGRANZA because I need binary vectors.
$endgroup$
– V. Gai
Dec 20 '18 at 12:56
$begingroup$
@RobertIsrael may be you can send me link to book which explains how can I prove, that some set with operations, defined on it, is Boolean algebra?
$endgroup$
– V. Gai
Dec 20 '18 at 12:58
1
1
$begingroup$
Yes, that's right.
$endgroup$
– Robert Israel
Dec 20 '18 at 12:54
$begingroup$
Yes, that's right.
$endgroup$
– Robert Israel
Dec 20 '18 at 12:54
$begingroup$
@MauroALLEGRANZA because I need binary vectors.
$endgroup$
– V. Gai
Dec 20 '18 at 12:56
$begingroup$
@MauroALLEGRANZA because I need binary vectors.
$endgroup$
– V. Gai
Dec 20 '18 at 12:56
$begingroup$
@RobertIsrael may be you can send me link to book which explains how can I prove, that some set with operations, defined on it, is Boolean algebra?
$endgroup$
– V. Gai
Dec 20 '18 at 12:58
$begingroup$
@RobertIsrael may be you can send me link to book which explains how can I prove, that some set with operations, defined on it, is Boolean algebra?
$endgroup$
– V. Gai
Dec 20 '18 at 12:58
add a comment |
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1
$begingroup$
Yes, that's right.
$endgroup$
– Robert Israel
Dec 20 '18 at 12:54
$begingroup$
@MauroALLEGRANZA because I need binary vectors.
$endgroup$
– V. Gai
Dec 20 '18 at 12:56
$begingroup$
@RobertIsrael may be you can send me link to book which explains how can I prove, that some set with operations, defined on it, is Boolean algebra?
$endgroup$
– V. Gai
Dec 20 '18 at 12:58