Relations
Types of Relations
AIEEE 2004
Grade 11
Question:
Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on $A = \{1, 2, 3, 4\}$. $R$ is:
(1) a function
(2) transitive
(3) not symmetric
(4) reflexive
Step-by-Step Solution
Key Concept: $(2, 3) \in R$ but $(3, 2) \notin R$, so $R$ is not symmetric. $(1, 1) \notin R$ so not reflexive. $(4, 2)$ and $(2, 4)$ are both in $R$ but $(4, 4) \notin R$, so not transitive. Not a function since 2 maps to both 4 and 3.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)