var ax = new[] { new A { Id = 1, Name = "A" }, new A { Id = 2, Name = "B" } };
var ay = new[] { new B { Id = 1, Age = 10 }, new B { Id = 3, Age = 20 }, new B { Id = 5, Age = 30 } };

var x = ax.Select(s => new { s.Id, s.Name, Age = -1 });
var y = ay.Select(s => new { s.Id, Name = string.Empty, s.Age });

var q1 = x.GroupJoin(y, x1 => x1, y1 => y1, (value, temp) => value);
var q2 = y.GroupJoin(x, y1 => y1, x1 => x1, (value, temp) => value);

// full outer join
var q3 = q1.Union(q2);

// cross join
var q4 = from ax1 in ax
        from ay1 in ay
        select new { a1 = ax1.Id, a2 = ax1.Name, a3 = ay1.Id, a4 = ay1.Age };

var x = new[] { 1, 2, };
var y = new[] { 1, 2, 3,  };

var q1 = x.GroupJoin(y, x1 => x1, y1 => y1, (value, temp) => value);
var q2 = y.GroupJoin(x, y1 => y1, x1 => x1, (value, temp) => value);

// full outer join (1, 2, 3), итого 3 строки
var q3 = q1.Union(q2);

// cross join (1;1, 1;2, 1;3, 2;1, 2;2, 2;3), итого 6 строк
var q4 = from x1 in x
            from y1 in y
            select new { x1, y1 };

create table #A (Id int, Name nvarchar(max))
create table #B (Id int, Age int)

INSERT #A VALUES (1, 'A')
INSERT #A VALUES (2, 'B')
INSERT #B VALUES (1, 10)
INSERT #B VALUES (3, 20)

SELECT *
FROM #A FULL JOIN #B ON #A.Id=#B.Id

drop table #A
drop table #B

SELECT ISNULL(#A.Id, #B.Id), #A.Name, #B.Age

INSERT @A VALUES (1, 'A')
INSERT @A VALUES (2, 'B')
INSERT @B VALUES (1, 10)
INSERT @B VALUES (3, 20)

SELECT * FROM @A A FULL JOIN @B B ON A.Id=B.Id

var ax = new[] { new A { Id = 1, Name = "A" }, new A { Id = 2, Name = "B" } };
var ay = new[] { new B { Id = 1, Age = 10 }, new B { Id = 3, Age = 20 }, new B { Id = 5, Age = 30 } };

var x = ax.Select(s => new { s.Id, s.Name, Age = -1 });
var y = ay.Select(s => new { s.Id, Name = string.Empty, s.Age });

var q1 = x.GroupJoin(y, x1 => x1, y1 => y1, (value, temp) => value);
var q2 = y.GroupJoin(x, y1 => y1, x1 => x1, (value, temp) => value);

// full outer join
var q3 = q1.Union(q2);

// cross join
var q4 = from ax1 in ax
        from ay1 in ay
        select new { a1 = ax1.Id, a2 = ax1.Name, a3 = ay1.Id, a4 = ay1.Age };

var ax = new[] { new A { Id = 1, Name = "A" }, new A { Id = 2, Name = "B" } };
var ay = new[] { new B { Id = 1, Age = 10 }, new B { Id = 3, Age = 20 }, new B { Id = 5, Age = 30 } };

INSERT @A VALUES (1, 'A')
INSERT @A VALUES (2, 'B')
INSERT @B VALUES (1, 10)
INSERT @B VALUES (3, 20)

// full outer join
var q3 = q1.Union(q2);

// cross join
var q4 = from ax1 in ax
        from ay1 in ay
        select new { a1 = ax1.Id, a2 = ax1.Name, a3 = ay1.Id, a4 = ay1.Age };

var x = new[] { new A { Id = 1, Name = "Вася" }, new A { Id = 2, Name = "Макар" }, new A { Id = 4, Name = "Петя" } };
var y = new[] { new A { Id = 1, Name = "Вася" }, new A { Id = 3, Name = "Иван" }, new A { Id = 4, Name = "Петя" }, new A { Id = 5, Name = "Никита" } };

var q1 = x.GroupJoin(y, x1 => x1.Id, y1 => y1.Id, (value, temp) => new { a = value.Id, b = value.Name, c = temp.FirstOrDefault() == null ? null : (int?) temp.FirstOrDefault().Id });
var q2 = y.GroupJoin(x, y1 => y1.Id, x1 => x1.Id, (value, temp) => new { a = value.Id, b = value.Name, c = temp.FirstOrDefault() == null ? null : (int?)temp.FirstOrDefault().Id });

// full outer join
var q3 = q1.Union(q2);

// cross join
var q4 = from ax1 in x
            from ay1 in y
            select new { ax1, ay1 };