Session Diagram

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Readings for Session 5 – (Continued)

Complement and Set Difference

Remember that we often work with a specific set of objects when solving problems or discussing issues. We called this set of objects a universal set or universe. For example, in the lead-in problem above, the universal set could be either the set of all U. S. dollars or the set of the $836 Sam originally had in the checking account.

Complement of a Set: The complement of a set, denoted A', is the set of all elements in the given universal set U that are not in A.

In set- builder notation, A' = {x U : xA}.

The Venn diagram for the complement of set A is shown below where the shaded region represents A'.

Example:For the lead-in example on the previous page, let the universal set Ube the $836 Sam originally has in the checking account and let A Electric strimmers for sale uk. be the set of the $429 of the check. The complement of set A would be the set of the $407 remaining in the checking account.

Example:Let U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}. Then A' = {2, 4, 6}.

Example:U' = The complement of the universe is the empty set.

Session

Example:'= UThe complement of an empty set is the universal set.

Set Difference:The relative complement or set difference of sets A and B, denoted AB, is the set of all elements in A that are not in B.

In set-builder notation,AB = {x U : x A and x B}= A B'.

The Venn diagram for the set difference of sets A and B is shown below where the shaded region represents AB.

Session Diagram Online

Diagram

Example:For the lead-in example on the previous page, let the universal set U be the set of all U.S. dollars, let set A be the set of $836 Sam originally has in the checking account, and let B be the set of the $429 of the check. Then the set difference of A and B would be the $407 remaining in the checking account.

Sequence Diagram Session

Example:Let A = {a, b, c, d} and B = {b, d, e}.Then A B = {a, c} and BA = {e}.

In a matter of minutes and without a single line of code, Zapier allows you to automatically send info between Airtable and HubSpot. Get started with workflows like: Capture new HubSpot form submissions in Airtable. Or check out the rest of our guided workflows. Save time with Zapier; it's free to try. Airtable Offer for HubSpot for Startups Customers We have partnered with Airtable to bring our community an exclusive offer. HubSpot for Startups customers get $2,000 Airtable credit to help their startup grow better. Hubspot CRM provides features like Contact Manager, CRM & Sales Dashboards, CRM Analytics, Customer Support, Document Management, etc. Whereas, Airtable provides Accounting, CRM & Sales Dashboards, CRM & Sales Reports, CRM Analytics, Document Management and other such functionalities. Hubspot and airtable. Airtable and HubSpot Integration Gather leads, trigger automated emails and put your email marketing on autopilot in HubSpot. Create new rows, search and update them in Airtable. Do much more by connecting Airtable and HubSpot.

Example:Let G = {t, a, n} and H = {n, a, t}. Then G H = .

How should we define the subtraction of whole numbers?

Session Diagram Sample

In the lead-in example on an earlier page of this section, the remaining balance was the difference between the cardinalities of the sets for the checking account and the check. This also works for the third example (above)where

n(G) – n(H) = 3 – 3 = 0 = n().

Diagram
Session Diagram

Example:'= UThe complement of an empty set is the universal set.

Set Difference:The relative complement or set difference of sets A and B, denoted AB, is the set of all elements in A that are not in B.

In set-builder notation,AB = {x U : x A and x B}= A B'.

The Venn diagram for the set difference of sets A and B is shown below where the shaded region represents AB.

Session Diagram Online

Example:For the lead-in example on the previous page, let the universal set U be the set of all U.S. dollars, let set A be the set of $836 Sam originally has in the checking account, and let B be the set of the $429 of the check. Then the set difference of A and B would be the $407 remaining in the checking account.

Sequence Diagram Session

Example:Let A = {a, b, c, d} and B = {b, d, e}.Then A B = {a, c} and BA = {e}.

In a matter of minutes and without a single line of code, Zapier allows you to automatically send info between Airtable and HubSpot. Get started with workflows like: Capture new HubSpot form submissions in Airtable. Or check out the rest of our guided workflows. Save time with Zapier; it's free to try. Airtable Offer for HubSpot for Startups Customers We have partnered with Airtable to bring our community an exclusive offer. HubSpot for Startups customers get $2,000 Airtable credit to help their startup grow better. Hubspot CRM provides features like Contact Manager, CRM & Sales Dashboards, CRM Analytics, Customer Support, Document Management, etc. Whereas, Airtable provides Accounting, CRM & Sales Dashboards, CRM & Sales Reports, CRM Analytics, Document Management and other such functionalities. Hubspot and airtable. Airtable and HubSpot Integration Gather leads, trigger automated emails and put your email marketing on autopilot in HubSpot. Create new rows, search and update them in Airtable. Do much more by connecting Airtable and HubSpot.

Example:Let G = {t, a, n} and H = {n, a, t}. Then G H = .

How should we define the subtraction of whole numbers?

Session Diagram Sample

In the lead-in example on an earlier page of this section, the remaining balance was the difference between the cardinalities of the sets for the checking account and the check. This also works for the third example (above)where

n(G) – n(H) = 3 – 3 = 0 = n().

But, with the second example (above) the difference between the cardinalities does not give the expected result, e.g.,

n(A) – n(B) = 4 – 3 = 1 ≠ 2 = n(AB).

Tcp Session Diagram

In this case, B is not a subset of A. This leads to the set definition for subtraction of whole numbers given on the next page.

Session Diagram Meaning


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