Discrete math predicate problem
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In this problem, we will be using binary predicates F(x, y), G(x, y), etc. to represent functions f, g : U → U, etc., where U is the universe. Thus, F(x, y) holds iff y = f(x), G(x, y) holds iff y = g(x), etc.
- Write predicate statements that expresses the following facts:
- F represents a function.
- F represents a one-to-one function.
- F represents an onto function.
- F and G represent inverse functions of one another.
- H represents the composition function $f circ g$.
- Use binary predicates representing functions to give formal proofs (in the style of Sec 1.6 of the following statements:
- “If f and g are one-to-one functions, then so is $f circ g$.”
- “If f and g are onto functions, then so is $f circ g$.”
functions discrete-mathematics logic
edited Dec 4 at 16:18
gt6989b
32.7k22451
asked Dec 4 at 16:08
Mohamed Mahfouz
1
add a comment |
up vote
0
down vote
favorite
In this problem, we will be using binary predicates F(x, y), G(x, y), etc. to represent functions f, g : U → U, etc., where U is the universe. Thus, F(x, y) holds iff y = f(x), G(x, y) holds iff y = g(x), etc.
- Write predicate statements that expresses the following facts:
- F represents a function.
- F represents a one-to-one function.
- F represents an onto function.
- F and G represent inverse functions of one another.
- H represents the composition function $f circ g$.
- Use binary predicates representing functions to give formal proofs (in the style of Sec 1.6 of the following statements:
- “If f and g are one-to-one functions, then so is $f circ g$.”
- “If f and g are onto functions, then so is $f circ g$.”
functions discrete-mathematics logic
edited Dec 4 at 16:18
gt6989b
32.7k22451
asked Dec 4 at 16:08
Mohamed Mahfouz
1
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 at 22:09
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In this problem, we will be using binary predicates F(x, y), G(x, y), etc. to represent functions f, g : U → U, etc., where U is the universe. Thus, F(x, y) holds iff y = f(x), G(x, y) holds iff y = g(x), etc.
- Write predicate statements that expresses the following facts:
- F represents a function.
- F represents a one-to-one function.
- F represents an onto function.
- F and G represent inverse functions of one another.
- H represents the composition function $f circ g$.
- Use binary predicates representing functions to give formal proofs (in the style of Sec 1.6 of the following statements:
- “If f and g are one-to-one functions, then so is $f circ g$.”
- “If f and g are onto functions, then so is $f circ g$.”
functions discrete-mathematics logic
edited Dec 4 at 16:18
gt6989b
32.7k22451
asked Dec 4 at 16:08
Mohamed Mahfouz
1
In this problem, we will be using binary predicates F(x, y), G(x, y), etc. to represent functions f, g : U → U, etc., where U is the universe. Thus, F(x, y) holds iff y = f(x), G(x, y) holds iff y = g(x), etc.
- Write predicate statements that expresses the following facts:
- F represents a function.
- F represents a one-to-one function.
- F represents an onto function.
- F and G represent inverse functions of one another.
- H represents the composition function $f circ g$.
- Use binary predicates representing functions to give formal proofs (in the style of Sec 1.6 of the following statements:
- “If f and g are one-to-one functions, then so is $f circ g$.”
- “If f and g are onto functions, then so is $f circ g$.”
functions discrete-mathematics logic
functions discrete-mathematics logic
edited Dec 4 at 16:18
gt6989b
32.7k22451
asked Dec 4 at 16:08
Mohamed Mahfouz
1
edited Dec 4 at 16:18
gt6989b
32.7k22451
asked Dec 4 at 16:08
Mohamed Mahfouz
1
edited Dec 4 at 16:18
gt6989b
32.7k22451
edited Dec 4 at 16:18
gt6989b
32.7k22451
edited Dec 4 at 16:18
gt6989b
32.7k22451
32.7k22451
asked Dec 4 at 16:08
Mohamed Mahfouz
1
asked Dec 4 at 16:08
Mohamed Mahfouz
1
asked Dec 4 at 16:08
Mohamed Mahfouz
1
1
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 at 22:09
add a comment |
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 at 22:09
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 at 16:18
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 at 22:05
Would you describe the style of section 1.6?
– William Elliot
Dec 4 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 at 22:09
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 at 22:09
add a comment |
1 Answer
1
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0
down vote
I'll do the very first one ... see if that helps you get some of the others:
$F$ represents a function:
$neg exists x exists y exists z (F(x,y) land F(x,z) land neg y = z)$
or, equivalently:
$forall x forall y forall z ((F(x,y) land F(x,z)) rightarrow y=z)$
or, equivalently:
$forall x forall y (F(x,y) rightarrow neg exists z ( F(x,z) land neg y = z))$
or, equivalently:
$forall x forall y (F(x,y) rightarrow forall z ( F(x,z) rightarrow y = z))$
answered Dec 5 at 1:36
Bram28
59.1k44186
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
add a comment |
Your Answer
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
I'll do the very first one ... see if that helps you get some of the others:
$F$ represents a function:
$neg exists x exists y exists z (F(x,y) land F(x,z) land neg y = z)$
or, equivalently:
$forall x forall y forall z ((F(x,y) land F(x,z)) rightarrow y=z)$
or, equivalently:
$forall x forall y (F(x,y) rightarrow neg exists z ( F(x,z) land neg y = z))$
or, equivalently:
$forall x forall y (F(x,y) rightarrow forall z ( F(x,z) rightarrow y = z))$
answered Dec 5 at 1:36
Bram28
59.1k44186
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
add a comment |
up vote
0
down vote
I'll do the very first one ... see if that helps you get some of the others:
$F$ represents a function:
$neg exists x exists y exists z (F(x,y) land F(x,z) land neg y = z)$
or, equivalently:
$forall x forall y forall z ((F(x,y) land F(x,z)) rightarrow y=z)$
or, equivalently:
$forall x forall y (F(x,y) rightarrow neg exists z ( F(x,z) land neg y = z))$
or, equivalently:
$forall x forall y (F(x,y) rightarrow forall z ( F(x,z) rightarrow y = z))$
answered Dec 5 at 1:36
Bram28
59.1k44186
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
add a comment |
up vote
0
down vote
up vote
0
down vote
I'll do the very first one ... see if that helps you get some of the others:
$F$ represents a function:
$neg exists x exists y exists z (F(x,y) land F(x,z) land neg y = z)$
or, equivalently:
$forall x forall y forall z ((F(x,y) land F(x,z)) rightarrow y=z)$
or, equivalently:
$forall x forall y (F(x,y) rightarrow neg exists z ( F(x,z) land neg y = z))$
or, equivalently:
$forall x forall y (F(x,y) rightarrow forall z ( F(x,z) rightarrow y = z))$
answered Dec 5 at 1:36
Bram28
59.1k44186
I'll do the very first one ... see if that helps you get some of the others:
$F$ represents a function:
$neg exists x exists y exists z (F(x,y) land F(x,z) land neg y = z)$
or, equivalently:
$forall x forall y forall z ((F(x,y) land F(x,z)) rightarrow y=z)$
or, equivalently:
$forall x forall y (F(x,y) rightarrow neg exists z ( F(x,z) land neg y = z))$
or, equivalently:
$forall x forall y (F(x,y) rightarrow forall z ( F(x,z) rightarrow y = z))$
answered Dec 5 at 1:36
Bram28
59.1k44186
edited Dec 5 at 3:15
answered Dec 5 at 1:36
Bram28
59.1k44186
answered Dec 5 at 1:36
Bram28
59.1k44186
answered Dec 5 at 1:36
Bram28
59.1k44186
59.1k44186
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
add a comment |
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 at 3:13
add a comment |
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Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 at 22:09