Discrete math predicate problem
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 '18 at 16:18
gt6989b
33.1k22452
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
add a comment |
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 '18 at 16:18
gt6989b
33.1k22452
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 '18 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 '18 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 '18 at 22:09
add a comment |
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 '18 at 16:18
gt6989b
33.1k22452
asked Dec 4 '18 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 '18 at 16:18
gt6989b
33.1k22452
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
edited Dec 4 '18 at 16:18
gt6989b
33.1k22452
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
edited Dec 4 '18 at 16:18
gt6989b
33.1k22452
edited Dec 4 '18 at 16:18
gt6989b
33.1k22452
edited Dec 4 '18 at 16:18
gt6989b
33.1k22452
33.1k22452
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
asked Dec 4 '18 at 16:08
Mohamed Mahfouz
1
1
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 '18 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 '18 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 '18 at 22:09
add a comment |
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 '18 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 '18 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 '18 at 22:09
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 '18 at 16:18
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 '18 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 '18 at 22:05
Would you describe the style of section 1.6?
– William Elliot
Dec 4 '18 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 '18 at 22:09
add a comment |
1 Answer
1
active
oldest
votes
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 '18 at 1:36
Bram28
60.3k44590
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3025749%2fdiscrete-math-predicate-problem%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 '18 at 1:36
Bram28
60.3k44590
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
add a comment |
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 '18 at 1:36
Bram28
60.3k44590
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
add a comment |
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 '18 at 1:36
Bram28
60.3k44590
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 '18 at 1:36
Bram28
60.3k44590
edited Dec 5 '18 at 3:15
answered Dec 5 '18 at 1:36
Bram28
60.3k44590
answered Dec 5 '18 at 1:36
Bram28
60.3k44590
answered Dec 5 '18 at 1:36
Bram28
60.3k44590
60.3k44590
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
add a comment |
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
@WilliamElliot I thought I had that one! :)
– Bram28
Dec 5 '18 at 3:13
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3025749%2fdiscrete-math-predicate-problem%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Welcome to Math.SE! Where are you getting stuck exactly?
– gt6989b
Dec 4 '18 at 16:18
Would you describe the style of section 1.6?
– William Elliot
Dec 4 '18 at 22:05
@WilliamElliot It's about rules of inference from Rosen Discrete Math and its applications
– Mohamed Mahfouz
Dec 4 '18 at 22:09
@gt6989b am really stuck don't understand the problem
– Mohamed Mahfouz
Dec 4 '18 at 22:09