Logic?
Algebra
Level
4
Consider the dictionary. Let the words in the dictionary be placed under a set,A. Now, a relation is defined such that R(A to A)={(x,y)} such that x and y have atleast on letter in common. Then, R is ?
Only symmetric
Only reflexive
transitive and symmetric
Reflexive and symmetric
Equivalence
transitive and reflexive
Only transitive
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1 solution
The only was is to take an example and disprove transitive nature.
Example (cat,bat) and (bat,bull) satisfy the relation but (cat,bull) doesnt satisfy. so, it is intransitive and moreover it is always reflexive and symmetric as (bat,cat) also belongs to the set and (cat,cat) also belongs to the set.
So, this is a simple logic question where we have to use contradiction.