Push notifications related to the community are not available within the Salesforce mobile app.

Answer options:

A.Yes
B.No

Correct Answer: A 
Salesforce communities have full features through the website. But through the mobile apps, there are some limitations where push notifications are not supported yet. 
Reference: 

https://help.salesforce.com/articleView?id=limits_mobile_sf1_communities.htm&type=5