Which of the following relations are transitive?
Which of the following relations are transitive?
The correct options are
A "Shares birthday with" on set of people
C "Is greater than" on a set of numbers
D "Is elder to" on a set of people
Let's go through the options and check if the relations given are transitive.
A) Shares birthday with: If a and b has same birthday on same day and b and c has birthday on same day then a and c will have birthday on the same day. This is the condition for the relation to be transitive. This is true because all the three people a,b and c will have birthday on the same day if we are given a and b have same birthday and b and c have same birthday
B) Is friends on Facebook with: I have a friend Rakesh and let's assume me and you are friends. So, from the relations point of view, You are related to me and I am related to Rakesh. But do you even know my friend Rakesh. We can’t say you and Rakesh are related, which makes the relation not transitive
C) If a is greater than b and b is greater than c, then we can say a is greater than c. So the given relation is transitive.
D) This is similar to the previous relation. If we say a is elder than b and b is elder than c, then we can say that a is elder than c. This is also an example of transitive relation.
A
"Shares birthday with" on set of people
C
"Is greater than" on a set of numbers
D
"Is elder to" on a set of people
Let's go through the options and check if the relations given are transitive.
A) Shares birthday with: If a and b has same birthday on same day and b and c has birthday on same day then a and c will have birthday on the same day. This is the condition for the relation to be transitive. This is true because all the three people a,b and c will have birthday on the same day if we are given a and b have same birthday and b and c have same birthday
B) Is friends on Facebook with: I have a friend Rakesh and let's assume me and you are friends. So, from the relations point of view, You are related to me and I am related to Rakesh. But do you even know my friend Rakesh. We can’t say you and Rakesh are related, which makes the relation not transitive
C) If a is greater than b and b is greater than c, then we can say a is greater than c. So the given relation is transitive.
D) This is similar to the previous relation. If we say a is elder than b and b is elder than c, then we can say that a is elder than c. This is also an example of transitive relation.
