Relations & Functions
Power set; superset relation properties
MMTS_Full_Test_17
Grade 12
Question:
Let $P(A)$ be defined as power set of set $A=\{1,2,3,\ldots,2025\}$. Let $R$ be a relation defined on $P(A)$ as $(B,C)\in R$ if $B$ is superset of $C$, then $R$ is
(A) reflexive and transitive relation
(B) reflexive and symmetric relation
(C) symmetric and transitive relation
(D) equivalence relation
Step-by-Step Solution
Key Concept: Reflexive: $B\supseteq B$ ✓. Not symmetric: $B\supseteq C$ does not imply $C\supseteq B$. Transitive: $B\supseteq C$ and $C\supseteq D$ $\Rightarrow$ $B\supseteq D$ ✓.
Reflexive and transitive only.
Correct Answer: (A) reflexive and transitive relation