For the negation of statement
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âÂÂy â Z such that âÂÂx â Z, R(x + y)
âÂÂx â Z, âÂÂy â Z such that R(x + y)
Base on this two rule
"For all x, A(x)" negation:"There exist x such that not A(x)"
"There exists x such that A(x)" negation:"For every x, not A(x)"
what I did is "âÂÂy â Z, not âÂÂx â Z, R(x + y)"
"âÂÂx â Z, âÂÂy â Z such that R(x + y) "
I wish anyone could help me to check whether this is right or not. Thank you!
discrete-mathematics
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up vote
0
down vote
favorite
âÂÂy â Z such that âÂÂx â Z, R(x + y)
âÂÂx â Z, âÂÂy â Z such that R(x + y)
Base on this two rule
"For all x, A(x)" negation:"There exist x such that not A(x)"
"There exists x such that A(x)" negation:"For every x, not A(x)"
what I did is "âÂÂy â Z, not âÂÂx â Z, R(x + y)"
"âÂÂx â Z, âÂÂy â Z such that R(x + y) "
I wish anyone could help me to check whether this is right or not. Thank you!
discrete-mathematics
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
âÂÂy â Z such that âÂÂx â Z, R(x + y)
âÂÂx â Z, âÂÂy â Z such that R(x + y)
Base on this two rule
"For all x, A(x)" negation:"There exist x such that not A(x)"
"There exists x such that A(x)" negation:"For every x, not A(x)"
what I did is "âÂÂy â Z, not âÂÂx â Z, R(x + y)"
"âÂÂx â Z, âÂÂy â Z such that R(x + y) "
I wish anyone could help me to check whether this is right or not. Thank you!
discrete-mathematics
âÂÂy â Z such that âÂÂx â Z, R(x + y)
âÂÂx â Z, âÂÂy â Z such that R(x + y)
Base on this two rule
"For all x, A(x)" negation:"There exist x such that not A(x)"
"There exists x such that A(x)" negation:"For every x, not A(x)"
what I did is "âÂÂy â Z, not âÂÂx â Z, R(x + y)"
"âÂÂx â Z, âÂÂy â Z such that R(x + y) "
I wish anyone could help me to check whether this is right or not. Thank you!
discrete-mathematics
asked Aug 19 at 11:55
TomSophicy
221
221
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2 Answers
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$forall yin Z text s.t. exists xin Z, text not R(x+y)$
$exists xin Z, forall yin Z, text s.t. not R(x+y)$
Thank you so much
â TomSophicy
Aug 19 at 12:24
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up vote
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The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$
Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
$forall yin Z text s.t. exists xin Z, text not R(x+y)$
$exists xin Z, forall yin Z, text s.t. not R(x+y)$
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
up vote
0
down vote
$forall yin Z text s.t. exists xin Z, text not R(x+y)$
$exists xin Z, forall yin Z, text s.t. not R(x+y)$
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
up vote
0
down vote
up vote
0
down vote
$forall yin Z text s.t. exists xin Z, text not R(x+y)$
$exists xin Z, forall yin Z, text s.t. not R(x+y)$
$forall yin Z text s.t. exists xin Z, text not R(x+y)$
$exists xin Z, forall yin Z, text s.t. not R(x+y)$
answered Aug 19 at 11:59
kevin
986
986
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
Thank you so much
â TomSophicy
Aug 19 at 12:24
Thank you so much
â TomSophicy
Aug 19 at 12:24
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
up vote
0
down vote
The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$
Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
up vote
0
down vote
The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$
Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
up vote
0
down vote
up vote
0
down vote
The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$
Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$
The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$
Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$
answered Aug 19 at 12:04
drhab
87.7k541119
87.7k541119
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
Thank you so much
â TomSophicy
Aug 19 at 12:24
Thank you so much
â TomSophicy
Aug 19 at 12:24
Thank you so much
â TomSophicy
Aug 19 at 12:24
add a comment |Â
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