Let $W$denotes the words in the English dictionary. Define the relation $R$ by $R = \{(x,\ y) \in W imes W:the\ world\ x\ and\ y\ have\ at\ least\ one\ letter\ in\ common\}$. Then, $R$ is

Question

Let $W$denotes the words in the English dictionary. Define the relation $R$ by $R = \{(x,\ y) \in W 	imes W:the\ world\ x\ and\ y\ have\ at\ least\ one\ letter\ in\ common\}$. Then, $R$ is

Dr. Abubacker · Accepted Answer

(a)
Let $W = \{ cat,\ toy,\ you,\ldots\}$
Clearly, $R$ is reflexive and symmetric but not transitive.
[Since, _{cat}R_{toy}, _{toy}R_{you}$
Rightarrow$ _{cat}R_{you}]

Q. Let $W$denotes the words in the English dictionary. Define the relation $R$ by $R = \{(x,\ y) \in W \times W:the\ world\ x\ and\ y\ have\ at\ least\ one\ letter\ in\ common\}$. Then, $R$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?