Negate the statement and re-express as an equivalent positive statement.
Need help with this homework problem. I need to negate the statement and then re-express it as a positive statement. I've searched online and haven't been able to find an answer. I'm having trouble grasping quantificational logic so thanks in advance to whoever helps.
Original statement:
Everyone is happy sometimes, but no one is happy all the time.
My attempt at symbolizing the statement: let x = be happy sometimes and y = to be happy all the time. ∀(x) ∧ ∃(¬y)
Any help is appreciated.
logic quantifiers
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
asked Dec 4 '18 at 2:36
bvallier
11
add a comment |
Need help with this homework problem. I need to negate the statement and then re-express it as a positive statement. I've searched online and haven't been able to find an answer. I'm having trouble grasping quantificational logic so thanks in advance to whoever helps.
Original statement:
Everyone is happy sometimes, but no one is happy all the time.
My attempt at symbolizing the statement: let x = be happy sometimes and y = to be happy all the time. ∀(x) ∧ ∃(¬y)
Any help is appreciated.
logic quantifiers
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
asked Dec 4 '18 at 2:36
bvallier
11
Do you need two negations, one for each, otr one single negation of the whole "original statement"?
– coffeemath
Dec 4 '18 at 2:41
2
You must have attempted to symbolize the original statement before negating it ... can you post your attempt?
– Bram28
Dec 4 '18 at 2:46
1
You really need a 2-var statement like $h(x,t)$ for $x$ is happy at time $t$ to symbolize these. Everyone happy sometime then is for all x exists t so h(x,t). no one happy all the time is then (not)[exists x) (for all t) h(x,t)], These can be put together using "and" for the "but" in original statement. [So far this has not been negated]
– coffeemath
Dec 4 '18 at 6:25
1
You cannot nagate variables: $x,y,ldots$. In quantificational logic (aka predicate logic) we have variables (to be quantified) and predicates. With them we form sentences and we have to use logical connective : $lnot, land, ldots$ with sentences.
– Mauro ALLEGRANZA
Dec 4 '18 at 7:11
add a comment |
Need help with this homework problem. I need to negate the statement and then re-express it as a positive statement. I've searched online and haven't been able to find an answer. I'm having trouble grasping quantificational logic so thanks in advance to whoever helps.
Original statement:
Everyone is happy sometimes, but no one is happy all the time.
My attempt at symbolizing the statement: let x = be happy sometimes and y = to be happy all the time. ∀(x) ∧ ∃(¬y)
Any help is appreciated.
logic quantifiers
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
asked Dec 4 '18 at 2:36
bvallier
11
Need help with this homework problem. I need to negate the statement and then re-express it as a positive statement. I've searched online and haven't been able to find an answer. I'm having trouble grasping quantificational logic so thanks in advance to whoever helps.
Original statement:
Everyone is happy sometimes, but no one is happy all the time.
My attempt at symbolizing the statement: let x = be happy sometimes and y = to be happy all the time. ∀(x) ∧ ∃(¬y)
Any help is appreciated.
logic quantifiers
logic quantifiers
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
asked Dec 4 '18 at 2:36
bvallier
11
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
asked Dec 4 '18 at 2:36
bvallier
11
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
edited Dec 4 '18 at 7:09
Mauro ALLEGRANZA
64.4k448112
64.4k448112
asked Dec 4 '18 at 2:36
bvallier
11
asked Dec 4 '18 at 2:36
bvallier
11
asked Dec 4 '18 at 2:36
bvallier
11
11
Do you need two negations, one for each, otr one single negation of the whole "original statement"?
– coffeemath
Dec 4 '18 at 2:41
2
You must have attempted to symbolize the original statement before negating it ... can you post your attempt?
– Bram28
Dec 4 '18 at 2:46
1
You really need a 2-var statement like $h(x,t)$ for $x$ is happy at time $t$ to symbolize these. Everyone happy sometime then is for all x exists t so h(x,t). no one happy all the time is then (not)[exists x) (for all t) h(x,t)], These can be put together using "and" for the "but" in original statement. [So far this has not been negated]
– coffeemath
Dec 4 '18 at 6:25
1
You cannot nagate variables: $x,y,ldots$. In quantificational logic (aka predicate logic) we have variables (to be quantified) and predicates. With them we form sentences and we have to use logical connective : $lnot, land, ldots$ with sentences.
– Mauro ALLEGRANZA
Dec 4 '18 at 7:11
add a comment |
Do you need two negations, one for each, otr one single negation of the whole "original statement"?
– coffeemath
Dec 4 '18 at 2:41
2
You must have attempted to symbolize the original statement before negating it ... can you post your attempt?
– Bram28
Dec 4 '18 at 2:46
1
You really need a 2-var statement like $h(x,t)$ for $x$ is happy at time $t$ to symbolize these. Everyone happy sometime then is for all x exists t so h(x,t). no one happy all the time is then (not)[exists x) (for all t) h(x,t)], These can be put together using "and" for the "but" in original statement. [So far this has not been negated]
– coffeemath
Dec 4 '18 at 6:25
1
You cannot nagate variables: $x,y,ldots$. In quantificational logic (aka predicate logic) we have variables (to be quantified) and predicates. With them we form sentences and we have to use logical connective : $lnot, land, ldots$ with sentences.
– Mauro ALLEGRANZA
Dec 4 '18 at 7:11
Do you need two negations, one for each, otr one single negation of the whole "original statement"?
– coffeemath
Dec 4 '18 at 2:41
Do you need two negations, one for each, otr one single negation of the whole "original statement"?
– coffeemath
Dec 4 '18 at 2:41
2
2
You must have attempted to symbolize the original statement before negating it ... can you post your attempt?
– Bram28
Dec 4 '18 at 2:46
You must have attempted to symbolize the original statement before negating it ... can you post your attempt?
– Bram28
Dec 4 '18 at 2:46
1
1
You really need a 2-var statement like $h(x,t)$ for $x$ is happy at time $t$ to symbolize these. Everyone happy sometime then is for all x exists t so h(x,t). no one happy all the time is then (not)[exists x) (for all t) h(x,t)], These can be put together using "and" for the "but" in original statement. [So far this has not been negated]
– coffeemath
Dec 4 '18 at 6:25
You really need a 2-var statement like $h(x,t)$ for $x$ is happy at time $t$ to symbolize these. Everyone happy sometime then is for all x exists t so h(x,t). no one happy all the time is then (not)[exists x) (for all t) h(x,t)], These can be put together using "and" for the "but" in original statement. [So far this has not been negated]
– coffeemath
Dec 4 '18 at 6:25
1
1
You cannot nagate variables: $x,y,ldots$. In quantificational logic (aka predicate logic) we have variables (to be quantified) and predicates. With them we form sentences and we have to use logical connective : $lnot, land, ldots$ with sentences.
– Mauro ALLEGRANZA
Dec 4 '18 at 7:11
You cannot nagate variables: $x,y,ldots$. In quantificational logic (aka predicate logic) we have variables (to be quantified) and predicates. With them we form sentences and we have to use logical connective : $lnot, land, ldots$ with sentences.
– Mauro ALLEGRANZA
Dec 4 '18 at 7:11
add a comment |
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Do you need two negations, one for each, otr one single negation of the whole "original statement"?
– coffeemath
Dec 4 '18 at 2:41
2
You must have attempted to symbolize the original statement before negating it ... can you post your attempt?
– Bram28
Dec 4 '18 at 2:46
1
You really need a 2-var statement like $h(x,t)$ for $x$ is happy at time $t$ to symbolize these. Everyone happy sometime then is for all x exists t so h(x,t). no one happy all the time is then (not)[exists x) (for all t) h(x,t)], These can be put together using "and" for the "but" in original statement. [So far this has not been negated]
– coffeemath
Dec 4 '18 at 6:25
1
You cannot nagate variables: $x,y,ldots$. In quantificational logic (aka predicate logic) we have variables (to be quantified) and predicates. With them we form sentences and we have to use logical connective : $lnot, land, ldots$ with sentences.
– Mauro ALLEGRANZA
Dec 4 '18 at 7:11