Studies examining children's basic understanding of conditionals have led to very different conclusions. On the one hand, conditional inference tasks suggest that young children are able to interpret familiar conditionals in a complex manner. In contrast, truth-table tasks suggest that before adolescence, children have limited (conjunctive) representations of conditionals. We hypothesized that the latter results are due to use of what are essentially arbitrary conditionals. To examine this, we gave a truth-table task using two kinds of conditional rules, Arbitrary and Imaginary categorical rules (If an animal is a bori, then it has red wings) to 9-and 12-yearolds. Results with the Arbitrary rules were consistent with those found in previous studies, with the most frequent interpretation being the Conjunctive one. However, among even the youngest children, the most frequent interpretation of the Imaginary categorical rules was the defective conditional, which is only found with much older adolescents with Arbitrary rules. These results suggest that working memory limitations are not an important developmental factor in how young children interpret conditional rules.