Database
db={"product":[{"_id":{"productId":{"$numberLong":"872223334"},"categoryCode":{"$numberLong":4}},"productName":"Decantor Jacket","category":"Plaid-Item","quantityInStock":{"$numberLong":4001}},{"_id":{"productId":{"$numberLong":"872223335"},"categoryCode":{"$numberLong":5}},"productName":"Decantor Shirt","category":"Plaid-Item","quantityInStock":{"$numberLong":4002}}]}
Query
db.product.aggregate([{$match:{$or:[{$and:[{"_id.productId":872223334},{"_id.categoryCode":4}]},{$and:[{"_id.productId":872223335},{"_id.categoryCode":5}]}]}}])