∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer
$begingroup$
∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer
Is the following a correct translation?
For all x, if x is an integer, then there exists an y such that y is an integer and x < y.
Is this a true or false statement? For numbers in R
discrete-mathematics predicate-logic quantifiers logic-translation
asked Jan 24 at 10:25
user635758user635758
163
$endgroup$
add a comment |
$begingroup$
∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer
Is the following a correct translation?
For all x, if x is an integer, then there exists an y such that y is an integer and x < y.
Is this a true or false statement? For numbers in R
discrete-mathematics predicate-logic quantifiers logic-translation
asked Jan 24 at 10:25
user635758user635758
163
$endgroup$
$begingroup$
"Is this a true or false statement?" Really no idea ?
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 11:00
add a comment |
$begingroup$
∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer
Is the following a correct translation?
For all x, if x is an integer, then there exists an y such that y is an integer and x < y.
Is this a true or false statement? For numbers in R
discrete-mathematics predicate-logic quantifiers logic-translation
asked Jan 24 at 10:25
user635758user635758
163
$endgroup$
∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer
Is the following a correct translation?
For all x, if x is an integer, then there exists an y such that y is an integer and x < y.
Is this a true or false statement? For numbers in R
discrete-mathematics predicate-logic quantifiers logic-translation
discrete-mathematics predicate-logic quantifiers logic-translation
asked Jan 24 at 10:25
user635758user635758
163
asked Jan 24 at 10:25
user635758user635758
163
edited Jan 24 at 10:35
user635758
asked Jan 24 at 10:25
user635758user635758
163
asked Jan 24 at 10:25
user635758user635758
163
asked Jan 24 at 10:25
user635758user635758
163
163
$begingroup$
"Is this a true or false statement?" Really no idea ?
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 11:00
add a comment |
$begingroup$
"Is this a true or false statement?" Really no idea ?
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 11:00
$begingroup$
"Is this a true or false statement?" Really no idea ?
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 11:00
$begingroup$
"Is this a true or false statement?" Really no idea ?
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 11:00
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Your translation is correct. Let $F_2(x,y)=x<y$,
$$forall x(I_1(x)toexists y(I_1(y)wedge F_2(x,y)))=forall x(overline{I_1(x)}veeexists y(I_1(y)wedge F_2(x,y)))=forall x(exists y(overline{I_1(x)}vee I_1(y))wedge exists y(overline{I_1(x)} vee F_2(x,y)))=forall xexists y(overline{I_1(x)}vee I_1(y))wedge forall xexists y(overline{I_1(x)} vee F_2(x,y))=[textrm{paste } I_1(x) textrm{ and } F_2(x,y);x,yin R]=(Tvee T) wedge(Tvee T)=T$$
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
$endgroup$
add a comment |
$begingroup$
Your translation is a direct symbol-by-symbol translation ... but no one actually speaks like that in English ... which is also why you have trouble understanding the sentence.
Here is a more fluent translation: "For every integer there is a greater integer"
Do you now see whether that is a true or false statement?
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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votes
active
oldest
votes
$begingroup$
Your translation is correct. Let $F_2(x,y)=x<y$,
$$forall x(I_1(x)toexists y(I_1(y)wedge F_2(x,y)))=forall x(overline{I_1(x)}veeexists y(I_1(y)wedge F_2(x,y)))=forall x(exists y(overline{I_1(x)}vee I_1(y))wedge exists y(overline{I_1(x)} vee F_2(x,y)))=forall xexists y(overline{I_1(x)}vee I_1(y))wedge forall xexists y(overline{I_1(x)} vee F_2(x,y))=[textrm{paste } I_1(x) textrm{ and } F_2(x,y);x,yin R]=(Tvee T) wedge(Tvee T)=T$$
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
$endgroup$
add a comment |
$begingroup$
Your translation is correct. Let $F_2(x,y)=x<y$,
$$forall x(I_1(x)toexists y(I_1(y)wedge F_2(x,y)))=forall x(overline{I_1(x)}veeexists y(I_1(y)wedge F_2(x,y)))=forall x(exists y(overline{I_1(x)}vee I_1(y))wedge exists y(overline{I_1(x)} vee F_2(x,y)))=forall xexists y(overline{I_1(x)}vee I_1(y))wedge forall xexists y(overline{I_1(x)} vee F_2(x,y))=[textrm{paste } I_1(x) textrm{ and } F_2(x,y);x,yin R]=(Tvee T) wedge(Tvee T)=T$$
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
$endgroup$
add a comment |
$begingroup$
Your translation is correct. Let $F_2(x,y)=x<y$,
$$forall x(I_1(x)toexists y(I_1(y)wedge F_2(x,y)))=forall x(overline{I_1(x)}veeexists y(I_1(y)wedge F_2(x,y)))=forall x(exists y(overline{I_1(x)}vee I_1(y))wedge exists y(overline{I_1(x)} vee F_2(x,y)))=forall xexists y(overline{I_1(x)}vee I_1(y))wedge forall xexists y(overline{I_1(x)} vee F_2(x,y))=[textrm{paste } I_1(x) textrm{ and } F_2(x,y);x,yin R]=(Tvee T) wedge(Tvee T)=T$$
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
$endgroup$
Your translation is correct. Let $F_2(x,y)=x<y$,
$$forall x(I_1(x)toexists y(I_1(y)wedge F_2(x,y)))=forall x(overline{I_1(x)}veeexists y(I_1(y)wedge F_2(x,y)))=forall x(exists y(overline{I_1(x)}vee I_1(y))wedge exists y(overline{I_1(x)} vee F_2(x,y)))=forall xexists y(overline{I_1(x)}vee I_1(y))wedge forall xexists y(overline{I_1(x)} vee F_2(x,y))=[textrm{paste } I_1(x) textrm{ and } F_2(x,y);x,yin R]=(Tvee T) wedge(Tvee T)=T$$
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
answered Jan 24 at 11:17
Yauhen MardanYauhen Mardan
936
936
add a comment |
add a comment |
$begingroup$
Your translation is a direct symbol-by-symbol translation ... but no one actually speaks like that in English ... which is also why you have trouble understanding the sentence.
Here is a more fluent translation: "For every integer there is a greater integer"
Do you now see whether that is a true or false statement?
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
$endgroup$
add a comment |
$begingroup$
Your translation is a direct symbol-by-symbol translation ... but no one actually speaks like that in English ... which is also why you have trouble understanding the sentence.
Here is a more fluent translation: "For every integer there is a greater integer"
Do you now see whether that is a true or false statement?
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
$endgroup$
add a comment |
$begingroup$
Your translation is a direct symbol-by-symbol translation ... but no one actually speaks like that in English ... which is also why you have trouble understanding the sentence.
Here is a more fluent translation: "For every integer there is a greater integer"
Do you now see whether that is a true or false statement?
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
$endgroup$
Your translation is a direct symbol-by-symbol translation ... but no one actually speaks like that in English ... which is also why you have trouble understanding the sentence.
Here is a more fluent translation: "For every integer there is a greater integer"
Do you now see whether that is a true or false statement?
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
answered Jan 24 at 16:02
Bram28Bram28
63.2k44793
63.2k44793
add a comment |
add a comment |
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$begingroup$
"Is this a true or false statement?" Really no idea ?
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 11:00