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I have following questions.<br />
<br />
1) Dir sync is used for migrating user accounts and passwords to office 365.<br />
If we have Dir sync ,and we have on premises 2013 server, can I log in to office 365 and on premises with &nbsp;same username and password.( Can we have single sign on)<br />
<br />
2) If this is true, then why should I have ADFS ?<br />
<br />
3) If I have on premises 2013 exchange server and o365 in hybrid mode.<br />
<br />
can I route mail flow directly from o365 to outside world instead of routing through on premiss exchange server.<br />
<br />
for that any steps needed.
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I have following questions.

1) Dir sync is used for migrating user accounts and passwords to office 365.
If we have Dir sync ,and we have on premises 2013 server, can I log in to office 365 and on premises with  same username and password.( Can we have single sign on)

2) If this is true, then why should I have ADFS ?

3) If I have on premises 2013 exchange server and o365 in hybrid mode.

can I route mail flow directly from o365 to outside world instead of routing through on premiss exchange server.

for that any steps needed.

0ffice 365

Office 365 is a group of software plus services subscriptions that provides productivity software and related services to its subscribers. Office 365 allows the use of Microsoft Office apps on Windows and OS X, provides storage space on Microsoft's cloud storage service OneDrive, and grants 60 Skype minutes per month. Office 365 includes e-mail and social networking services through hosted versions of Exchange Server, Skype for Business Server, SharePoint and Office Online, integration with Yammer, as well as access to the Office software. All of Office 365's components can be managed and configured through an online portal; users can be added manually, imported from a CSV file, or Office 365 can be set up for single sign-on with a local Active Directory using Active Directory Federation Services.

Microsoft 365

Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.

Exchange

Active Directory (AD) is a Microsoft brand for identity-related capabilities. In the on-premises world, Windows Server AD provides a set of identity capabilities and services, and is hugely popular (88% of Fortune 1000 and 95% of enterprises use AD). This topic includes all things Active Directory including DNS, Group Policy, DFS, troubleshooting, ADFS, and all other topics under the Microsoft AD and identity umbrella.