The article explores relationships in simple and 0-simple semihypergroups, focusing on the cardinality of these structures. They found all simple and 0-simple semihypergroups of order 3 where a specific relation is not transitive. The smallest order for a strongly simple semihypergroup with this relation not transitive is 4. They also discovered that another relation is always transitive in simple semihypergroups, and identified conditions for it to be transitive in 0-simple semihypergroups. These findings apply to semigroups as well.