mongodb $elemMatch

According to mongodb doc, syntax for $elemMatch would be,

t.find( { x : { $elemMatch : { a : 1, b : { $gt : 1 } } } } )

I have tried and it works fine.The above means that, it can find if an object {a:1, b:'more than 1'} exist in the array x.

I have a requirement, where I need to figure out, if all the objects in an array exist in the database or not.

for example, let's say I have an array,

a=[{a:1, b:2},{a:3, b:4}, {a:5, b:6}]

and I need to find out if x contains all of them.

t.find( { x : { $elemMatch : { a : {$all:[1]}, b : {$all:[2]} } } } ) and it finds out all x containing {a:1, b:2}

But if I try, t.find( { x : { $elemMatch : { a : {$all:[1,3]}, b : {$all:[2,4]} } } } ), it fails. I know this is not correct. Is there any way I can achieve this ?Ideallt, it should be,

t.find( { x : { $elemMatch : {$all:[ {a:1, b:2}, {a:3, b:4}] } } )

I tried, it does not work.