1. IETF RFC 2131
"Dynamic Host Configuration Protocol": The abstract and introduction (Section 1) state that DHCP's purpose is to provide a framework for passing configuration information
including the automatic allocation of network addresses
to hosts on a TCP/IP network. This directly supports option A.
2. IETF RFC 2132
"DHCP Options and BOOTP Vendor Extensions": Section 3.3
"Router Option
" explicitly defines an option (Code 3) for DHCP to provide a list of IP addresses for routers on the client's subnet. The first address is typically used as the default gateway
supporting option B.
3. MIT OpenCourseWare
6.033 Computer System Engineering
Spring 2018
Lecture 11 Notes: The section on "Dynamic Host Configuration Protocol (DHCP)" states
"DHCP can also tell the client the IP address of the local DNS resolver
the default gateway
etc." This confirms that providing the default gateway is a standard role of DHCP.