1. The problem asks to interpret the expression $B' \cup T'$ in the context of pupils playing basketball (B), cricket (C), and tennis (T). 2. Here, $B'$ represents the set of pupils who do not play basketball. 3. Similarly, $T'$ represents the set of pupils who do not play tennis. 4. The union $B' \cup T'$ means all pupils who either do not play basketball or do not play tennis (or both). 5. In terms of the Venn diagram, this includes all pupils outside the basketball circle, all pupils outside the tennis circle, and those outside both. 6. So, $B' \cup T'$ is the set of pupils who do not play basketball or do not play tennis, which means they might play cricket only, or no sport at all, or cricket and basketball but not tennis, etc., as long as they are not in both basketball and tennis simultaneously. 7. To summarize, $B' \cup T'$ represents all pupils who are not basketball players or not tennis players (including those who play cricket or none).