How to check if an array field contains a unique value or another array in MongoDB?

I am using mongodb now.

I have a blogpost collection, and it has a tags field which is an array, e.g.

blogpost1.tags = ['tag1', 'tag2', 'tag3', 'tag4', 'tag5']
blogpost2.tags = ['tag2', 'tag3']
blogpost3.tags = ['tag2', 'tag3', 'tag4', 'tag5']
blogpost4.tags = ['tag1', 'tag4', 'tag5']

How can I do these search

1. contains tag1
2. contains ['tag1','tag2']
3. contains any of ['tag3', 'tag4']

Try this out:

db.blogpost.find({ 'tags' : 'tag1'}); //1
db.blogpost.find({ 'tags' : { $all : [ 'tag1', 'tag2' ] }}); //2
db.blogpost.find({ 'tags' : { $in : [ 'tag3', 'tag4' ] }}); //3

My experience is that for (2) the following solution is much faster than the one with "$all":

db.blogpost.find({ $and: [ {tags: 'tag1'} ,{tags: 'tag2'} ] });

but to be honest, I do not not why. I would be interested in, if anyone knows.