Answer to Question #202041 in Discrete Mathematics for zain ul abdeen

Question

Q3:

List the 16 different relations on the set {0,1}.

Note: No partial credit would be admissible in this question.

Answer 1

Let us list the 16 different binary relations on the set $\{0,1\}$. Taking into account that $\{0,1\}\times\{0,1\}=\{(0,0),(0,1),(1,0),(1,1)\}$, we conclude that relations are following:

$R_1=\emptyset,\ R_2=\{(0,0)\},\ R_3=\{(0,1)\},\ R_4=\{(1,0)\},\ R_5=\{(1,1)\},\$

$R_6=\{(0,0),(0,1)\},\ R_7=\{(0,0),(1,0)\},\ R_8=\{(0,0),(1,1)\},\$

$R_9=\{(0,1),(1,0)\},\ R_{10}=\{(0,1),(1,1)\},\ R_{11}=\{(1,0),(1,1)\},\$

$R_{12}=\{(0,0),(0,1),(1,0)\},\ R_{13}=\{(0,0),(0,1),(1,1)\},\ R_{14}=\{(0,0),(1,1),(1,0)\},\$

$R_{15}=\{(1,1),(0,1),(1,0)\},\ R_{16}=\{(0,0),(0,1),(1,0),(1,1)\}.$