LINQ Join with Multiple Conditions in On Clause

I'm trying to implement a query in LINQ that uses a left outer join with multiple conditions in the ON clause.

I'll use the example of the following two tables Project (ProjectID, ProjectName) and Task (TaskID, ProjectID, TaskName, Completed). I want to see the f开发者_C百科ull list of all projects with their respective tasks, but only those tasks that are completed.

I cannot use a filter for Completed == true because that will filter out any projects that do not have completed tasks. Instead I want to add Completed == true to the ON clause of the join so that the full list of projects will be shown, but only completed tasks will be shown. Projects with no completed tasks will show a single row with a null value for Task.

Here's the foundation of the query.

from t1 in Projects
join t2 in Tasks
on new { t1.ProjectID} equals new { t2.ProjectID } into j1
from j2 in j1.DefaultIfEmpty()
select new { t1.ProjectName, t2.TaskName }

How do I add && t2.Completed == true to the on clause?

I can't seem to find any LINQ documentation on how to do this.

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You just need to name the anonymous property the same on both sides

on new { t1.ProjectID, SecondProperty = true } equals 
   new { t2.ProjectID, SecondProperty = t2.Completed } into j1

Based on the comments of @svick, here is another implementation that might make more sense:

from t1 in Projects
from t2 in Tasks.Where(x => t1.ProjectID == x.ProjectID && x.Completed == true)
                .DefaultIfEmpty()
select new { t1.ProjectName, t2.TaskName }

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Here you go with:

from b in _dbContext.Burden 
join bl in _dbContext.BurdenLookups on
new { Organization_Type = b.Organization_Type_ID, Cost_Type = b.Cost_Type_ID } equals
new { Organization_Type = bl.Organization_Type_ID, Cost_Type = bl.Cost_Type_ID }

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You can't do it like that. The join clause (and the Join() extension method) supports only equijoins. That's also the reason, why it uses equals and not ==. And even if you could do something like that, it wouldn't work, because join is an inner join, not outer join.