Ok so assume you've got a list of your CorpSystem objects in a variable called Corpsystems and a list of your AffectedSystem objects in a variable called AffectedSystems. Try the following:
Edit: For a join on all Affected Systems, try this:
var matches = from c in CorpSystems
join a in AffectedSystems on c.CorpSystemId equals a.CorpSystemId into ac
from subSystem in ac.DefaultIfEmpty()
select new
{
c.CorpSystemId,
c.SystemName,
Assigned = subSystem != null && subSystem.TaskItemId != null
};
Or for just AffectedSystems that have a TaskItemId of 1:
var matches = from c in CorpSystems
join a in AffectedSystems.Where(as => as.TaskItemId == 1)
on c.CorpSystemId equals a.CorpSystemId into ac
from subSystem in ac.DefaultIfEmpty()
select new
{
c.CorpSystemId,
c.SystemName,
Assigned = subSystem != null && subSystem.TaskItemId != null
};