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2

$begingroup$

This exercise is confusing me. Let $S(x,y,z):= $ $z$ is the child of $x$ and $y$, where $x$ is the mother and $y$ is the father. Express the following sentence in predicate logic using the predicate $S(x,y,z)$:

"There exist a being thats is a father or a mother of another being" $(1)$

My first thought was to write:
beginequation
exists xexists yexists z quad S(x,y,z)quad(2)
endequation
But then I realized that if there exists a being that only has a father and no being has a mother(I know it sounds stupid), then $(1)$ is true but not $(2)$.

Now I was thinking, what if we interpret the domain as $xin B, yin emptyset, zin B$, where $B$ is the set of beings and then write

$$exists xexists yexists z quad S(x,y,z)lor S(y,x,z)$$

Is this correct? Or am I confusing the meaning of logical interpretation?

logic first-order-logic predicate-logic quantifiers

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asked Mar 29 at 3:01

KashKash

895

$endgroup$

add a comment | 

2

$begingroup$

This exercise is confusing me. Let $S(x,y,z):= $ $z$ is the child of $x$ and $y$, where $x$ is the mother and $y$ is the father. Express the following sentence in predicate logic using the predicate $S(x,y,z)$:

"There exist a being thats is a father or a mother of another being" $(1)$

My first thought was to write:
beginequation
exists xexists yexists z quad S(x,y,z)quad(2)
endequation
But then I realized that if there exists a being that only has a father and no being has a mother(I know it sounds stupid), then $(1)$ is true but not $(2)$.

Now I was thinking, what if we interpret the domain as $xin B, yin emptyset, zin B$, where $B$ is the set of beings and then write

$$exists xexists yexists z quad S(x,y,z)lor S(y,x,z)$$

Is this correct? Or am I confusing the meaning of logical interpretation?

logic first-order-logic predicate-logic quantifiers

share|cite|improve this question

asked Mar 29 at 3:01

KashKash

895

$endgroup$

add a comment | 

$begingroup$

This exercise is confusing me. Let $S(x,y,z):= $ $z$ is the child of $x$ and $y$, where $x$ is the mother and $y$ is the father. Express the following sentence in predicate logic using the predicate $S(x,y,z)$:

"There exist a being thats is a father or a mother of another being" $(1)$

My first thought was to write:
beginequation
exists xexists yexists z quad S(x,y,z)quad(2)
endequation
But then I realized that if there exists a being that only has a father and no being has a mother(I know it sounds stupid), then $(1)$ is true but not $(2)$.

Now I was thinking, what if we interpret the domain as $xin B, yin emptyset, zin B$, where $B$ is the set of beings and then write

$$exists xexists yexists z quad S(x,y,z)lor S(y,x,z)$$

Is this correct? Or am I confusing the meaning of logical interpretation?

logic first-order-logic predicate-logic quantifiers

share|cite|improve this question

asked Mar 29 at 3:01

KashKash

895

$endgroup$

share|cite|improve this question

asked Mar 29 at 3:01

KashKash

895

share|cite|improve this question

asked Mar 29 at 3:01

KashKash

895

asked Mar 29 at 3:01

KashKash

895

asked Mar 29 at 3:01

KashKash

895