Set Builder Notation for all positive odd integers greater than or equal to 7
$begingroup$
A question in my text book for a course I'm taking over winter is asking me to give the set builder notation for (X∪Y)' [i.e. the complement of the union of set X and set Y] given that U=Z^+ [i.e. the universal set is that of all positive integers], X={1,2,3,4,5}, and Y={2n | n ∈ Z^+} [i.e. all positive even integers]. Basically, I'm looking for the set builder notation for the compliment of {1,2,3,4,5,6,8,10,12,14,...}.
I've figured out that the complement is {7,9,11,13,15,17,...}, or all positive odd integers greater-than or equal-to 7.
The issue is that the textbook doesn't give a very clear explanation as to what is and isn't correct when writing set builder notation. I've searched the internet for explanations and examples, but I've just been getting a lot of vague and/or conflicting information that doesn't tell me whether I've got the right set builder notation.
The answer that I have is (X∪Y)' = {n ∈ Z^+ | 2n+1 ≥ 7}.
Can someone tell me if this is correct? Or how I should change it if it isn't?
Thank you in advance!
discrete-mathematics
asked Jan 2 at 22:28
SeanSean
41
$endgroup$
add a comment |
$begingroup$
A question in my text book for a course I'm taking over winter is asking me to give the set builder notation for (X∪Y)' [i.e. the complement of the union of set X and set Y] given that U=Z^+ [i.e. the universal set is that of all positive integers], X={1,2,3,4,5}, and Y={2n | n ∈ Z^+} [i.e. all positive even integers]. Basically, I'm looking for the set builder notation for the compliment of {1,2,3,4,5,6,8,10,12,14,...}.
I've figured out that the complement is {7,9,11,13,15,17,...}, or all positive odd integers greater-than or equal-to 7.
The issue is that the textbook doesn't give a very clear explanation as to what is and isn't correct when writing set builder notation. I've searched the internet for explanations and examples, but I've just been getting a lot of vague and/or conflicting information that doesn't tell me whether I've got the right set builder notation.
The answer that I have is (X∪Y)' = {n ∈ Z^+ | 2n+1 ≥ 7}.
Can someone tell me if this is correct? Or how I should change it if it isn't?
Thank you in advance!
discrete-mathematics
asked Jan 2 at 22:28
SeanSean
41
$endgroup$
$begingroup$
Let's try to read what you wrote. ${nin Bbb Z^+mid 2n+1geq 7}$ is the set of all positive natural numbers such that if you were to double the amount and add one it would be greater than or equal to $7$. Unfortunately, that would correspond to the set ${3,4,5,6,7,dots}$ since $2n+1geq 7$ is true for $3$ since $2cdot 3 + 1geq 7$ and is also true for $4$ since $2cdot 4 + 1geq 7$ and so on.
$endgroup$
– JMoravitz
Jan 2 at 22:34
1
$begingroup$
There are many ways to write a correct answer here. One such way is to write it as ${2n+1 mid nin Bbb Z^+, ngeq 3}$. These are all numbers of the form $2n+1$ such that $n$ is a positive integer and $n$ is greater than or equal to $3$ (which makes $2n+1$ greater than or equal to $7$).
$endgroup$
– JMoravitz
Jan 2 at 22:37
add a comment |
$begingroup$
A question in my text book for a course I'm taking over winter is asking me to give the set builder notation for (X∪Y)' [i.e. the complement of the union of set X and set Y] given that U=Z^+ [i.e. the universal set is that of all positive integers], X={1,2,3,4,5}, and Y={2n | n ∈ Z^+} [i.e. all positive even integers]. Basically, I'm looking for the set builder notation for the compliment of {1,2,3,4,5,6,8,10,12,14,...}.
I've figured out that the complement is {7,9,11,13,15,17,...}, or all positive odd integers greater-than or equal-to 7.
The issue is that the textbook doesn't give a very clear explanation as to what is and isn't correct when writing set builder notation. I've searched the internet for explanations and examples, but I've just been getting a lot of vague and/or conflicting information that doesn't tell me whether I've got the right set builder notation.
The answer that I have is (X∪Y)' = {n ∈ Z^+ | 2n+1 ≥ 7}.
Can someone tell me if this is correct? Or how I should change it if it isn't?
Thank you in advance!
discrete-mathematics
asked Jan 2 at 22:28
SeanSean
41
$endgroup$
A question in my text book for a course I'm taking over winter is asking me to give the set builder notation for (X∪Y)' [i.e. the complement of the union of set X and set Y] given that U=Z^+ [i.e. the universal set is that of all positive integers], X={1,2,3,4,5}, and Y={2n | n ∈ Z^+} [i.e. all positive even integers]. Basically, I'm looking for the set builder notation for the compliment of {1,2,3,4,5,6,8,10,12,14,...}.
I've figured out that the complement is {7,9,11,13,15,17,...}, or all positive odd integers greater-than or equal-to 7.
The issue is that the textbook doesn't give a very clear explanation as to what is and isn't correct when writing set builder notation. I've searched the internet for explanations and examples, but I've just been getting a lot of vague and/or conflicting information that doesn't tell me whether I've got the right set builder notation.
The answer that I have is (X∪Y)' = {n ∈ Z^+ | 2n+1 ≥ 7}.
Can someone tell me if this is correct? Or how I should change it if it isn't?
Thank you in advance!
discrete-mathematics
discrete-mathematics
asked Jan 2 at 22:28
SeanSean
41
asked Jan 2 at 22:28
SeanSean
41
asked Jan 2 at 22:28
SeanSean
41
asked Jan 2 at 22:28
SeanSean
41
asked Jan 2 at 22:28
SeanSean
41
41
$begingroup$
Let's try to read what you wrote. ${nin Bbb Z^+mid 2n+1geq 7}$ is the set of all positive natural numbers such that if you were to double the amount and add one it would be greater than or equal to $7$. Unfortunately, that would correspond to the set ${3,4,5,6,7,dots}$ since $2n+1geq 7$ is true for $3$ since $2cdot 3 + 1geq 7$ and is also true for $4$ since $2cdot 4 + 1geq 7$ and so on.
$endgroup$
– JMoravitz
Jan 2 at 22:34
1
$begingroup$
There are many ways to write a correct answer here. One such way is to write it as ${2n+1 mid nin Bbb Z^+, ngeq 3}$. These are all numbers of the form $2n+1$ such that $n$ is a positive integer and $n$ is greater than or equal to $3$ (which makes $2n+1$ greater than or equal to $7$).
$endgroup$
– JMoravitz
Jan 2 at 22:37
add a comment |
$begingroup$
Let's try to read what you wrote. ${nin Bbb Z^+mid 2n+1geq 7}$ is the set of all positive natural numbers such that if you were to double the amount and add one it would be greater than or equal to $7$. Unfortunately, that would correspond to the set ${3,4,5,6,7,dots}$ since $2n+1geq 7$ is true for $3$ since $2cdot 3 + 1geq 7$ and is also true for $4$ since $2cdot 4 + 1geq 7$ and so on.
$endgroup$
– JMoravitz
Jan 2 at 22:34
1
$begingroup$
There are many ways to write a correct answer here. One such way is to write it as ${2n+1 mid nin Bbb Z^+, ngeq 3}$. These are all numbers of the form $2n+1$ such that $n$ is a positive integer and $n$ is greater than or equal to $3$ (which makes $2n+1$ greater than or equal to $7$).
$endgroup$
– JMoravitz
Jan 2 at 22:37
$begingroup$
Let's try to read what you wrote. ${nin Bbb Z^+mid 2n+1geq 7}$ is the set of all positive natural numbers such that if you were to double the amount and add one it would be greater than or equal to $7$. Unfortunately, that would correspond to the set ${3,4,5,6,7,dots}$ since $2n+1geq 7$ is true for $3$ since $2cdot 3 + 1geq 7$ and is also true for $4$ since $2cdot 4 + 1geq 7$ and so on.
$endgroup$
– JMoravitz
Jan 2 at 22:34
$begingroup$
Let's try to read what you wrote. ${nin Bbb Z^+mid 2n+1geq 7}$ is the set of all positive natural numbers such that if you were to double the amount and add one it would be greater than or equal to $7$. Unfortunately, that would correspond to the set ${3,4,5,6,7,dots}$ since $2n+1geq 7$ is true for $3$ since $2cdot 3 + 1geq 7$ and is also true for $4$ since $2cdot 4 + 1geq 7$ and so on.
$endgroup$
– JMoravitz
Jan 2 at 22:34
1
1
$begingroup$
There are many ways to write a correct answer here. One such way is to write it as ${2n+1 mid nin Bbb Z^+, ngeq 3}$. These are all numbers of the form $2n+1$ such that $n$ is a positive integer and $n$ is greater than or equal to $3$ (which makes $2n+1$ greater than or equal to $7$).
$endgroup$
– JMoravitz
Jan 2 at 22:37
$begingroup$
There are many ways to write a correct answer here. One such way is to write it as ${2n+1 mid nin Bbb Z^+, ngeq 3}$. These are all numbers of the form $2n+1$ such that $n$ is a positive integer and $n$ is greater than or equal to $3$ (which makes $2n+1$ greater than or equal to $7$).
$endgroup$
– JMoravitz
Jan 2 at 22:37
add a comment |
0
active
oldest
votes
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%2f3060048%2fset-builder-notation-for-all-positive-odd-integers-greater-than-or-equal-to-7%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
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%2f3060048%2fset-builder-notation-for-all-positive-odd-integers-greater-than-or-equal-to-7%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
$begingroup$
Let's try to read what you wrote. ${nin Bbb Z^+mid 2n+1geq 7}$ is the set of all positive natural numbers such that if you were to double the amount and add one it would be greater than or equal to $7$. Unfortunately, that would correspond to the set ${3,4,5,6,7,dots}$ since $2n+1geq 7$ is true for $3$ since $2cdot 3 + 1geq 7$ and is also true for $4$ since $2cdot 4 + 1geq 7$ and so on.
$endgroup$
– JMoravitz
Jan 2 at 22:34
1
$begingroup$
There are many ways to write a correct answer here. One such way is to write it as ${2n+1 mid nin Bbb Z^+, ngeq 3}$. These are all numbers of the form $2n+1$ such that $n$ is a positive integer and $n$ is greater than or equal to $3$ (which makes $2n+1$ greater than or equal to $7$).
$endgroup$
– JMoravitz
Jan 2 at 22:37