Require, no. Full and log can restore to a point in time. There are advantages and disadvantages to differentials, there are many places where they are useful.
Consider, for example, a scenario where a full backup takes 4 hours but the only time you have a 4 hour maintenance window is on a Sunday. What do you do for backups?
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)SQL In The Wild
: Discussions on DB performance with occasional diversions into recoverability
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