3 votes 3 votes Let $\text{S}$ be a non-empty set. $\text{P(s)}$ is the power set of $\text{S}.$ Let $\text{A}$ be a non-empty subset of $\text{P(s)}.$ We define “is subset of” relation $\text{R}$ on $\text{A}.$ So, $x\text{R}y$ iff $x$ is subset of $y.$ Which of the following is true? $\text{R}$ is necessarily reflexive. $\text{R}$ is necessarily transitive. It is possible for $\text{R}$ to be symmetric, for some choice of $\text{A}.$ It is possible for $\text{R}$ to be Not anti-symmetric, for some choice of $\text{A}.$ Set Theory & Algebra goclasses_wq7 goclasses set-theory&algebra set-theory relations multiple-selects 2-marks + – GO Classes asked Apr 14, 2022 • edited Apr 15, 2022 by Lakshman Bhaiya GO Classes 349 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Let $\text{S} = \{a,b\}$ Let $\text{A} = \{ \{a\} \}$ This $\text{A}$ is symmetric, antisymmetric, reflexive, transitive. Let $\text{S} = \{a,b\}$ Let $\text{A} = \{ \{a\}, \{a,b\} \}$ This $\text{A}$ is anti-symmetric, reflexive, transitive. GO Classes answered Apr 14, 2022 • edited Apr 14, 2022 by Lakshman Bhaiya GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
