[{"aaa":true,"bbb":111,},{"aaa":false,"bbb":111,}]

db.collection.aggregate([{"$group":{"_id":null,"sum":{"$sum":"$bbb"},"aaa_and":{"$sum":{"$cond":{"if":{"$eq":["$aaa",true]},"then":1,"else":0}}},"total":{$sum:1}}},{$project:{aaa_and:{"$eq":["$total","$aaa_and"]},aaa_or:{"$ne":["$aaa_and","0"]},sum:1}}])