As a major query type in SPARQL, ASK queries are boolean queries and have found applications in several domains such as semantic SPARQL optimization. This paper is a first systematic study of the relative expressive power of various fragments of ASK queries in SPARQL. Among many new results, a surprising one is that the operator UNION is redundant for ASK queries. The results in this paper as a whole paint a rich picture for the expressivity of fragments of ASK queries with the four basic operators of SPARQL 1.0 possibly together with a negation. The work in this paper provides a guideline for future SPARQL query optimization and implementation.