| Directions : (6 - 10) |
| Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin's sister Raji observed and noted the possible outcomes of the throw every time belongs to set \[\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\]. Let A be the set of players while B be the set of all possible outcomes. |
 |
| \[A=\left\{ S,\,D \right\},\,B=\left\{ 1,\,2,\,3,\,4,\,5,\,6 \right\}\] |
A) Reflexive and transitive but not symmetric
B) Reflexive and symmetric and not transitive
C) Not reflexive but symmetric and transitive
D) Equivalence
Correct Answer: A
Solution :
\[R=\left\{ \left( 1,\,1 \right),\,\left( 1,\,2 \right),\,\left( 1,3 \right),\,\left( 1,4 \right)\,\left( 1,\,5 \right),\,\left( 1,6 \right) \right.\] \[\left. \left( 2,\,2 \right),\,\left( 2,\,4 \right),\,\left( 2,\,6 \right),\,\left( 3,\,3 \right),\,\left( 3,\,6 \right),\,\left( 4,\,4 \right),\left( 5,5 \right),\,\left( 6,\,6 \right) \right\}\] here \[\left( a,\,a \right)\in R\,\,\forall \,\,a\,\,\in \,B\] \[\therefore \] R is reflexive Also \[\left( 1,\,\,2 \right)\in R\] but \[\left( 2,\,\,1 \right)-\notin \,R\] \[\therefore \] R is not symmetric Clearly \[\left( a,\,b \right)\in R,\,\left( b,\,c \right)\in R\Rightarrow \left( a,\,c \right)\in R\] \[\forall \,a,\,b,\,c\,\in B\] \[\therefore \] R is transitive.
You need to login to perform this action.
You will be redirected in
3 sec
