In the era of big data and cloud computing, outsourcing data storage to the cloud poses the risk of its abuse or leakage. Thus, we address the problem of delegating computation on outsourced private datasets while maintaining privacy. In this study, we consider a scenario involving two data owners outsourcing their datasets to a cloud service. The cloud performs a set union computation, after which the querier sends a query to obtain information from both datasets. We propose a protocol that uses fully homomorphic encryption (FHE) and Cartesian-join of Bloom filters (CBF) as proposed by Wang et al. The protocol obtains information on the existence of a particular set of elements without learning about the residing source. To the best of our knowledge, our protocol, by using the FHE and CBF matrix, is a novel approach to ensuring the security of outsourced set union operations.