Question

3) Check whether the relation R defined
in the set A of human beings in a town
at a particular time given by R= {x,y
X is exactly 7cm taller than y is an
equivalence relation
​

Answer 1

Answer:

R={(x,y):x is exactly 7 cm taller than y}

Now,

(x,x)∈   R

Since human being x cannot be taller than himself.

∴R is not reflexive.

Now, let (x,y)∈R.

⇒x is exactly 7cm taller than y

Then, y is not taller than x.

(y,x)∈   R

Indeed if x is exactly 7cm taller than y, then y is exactly 7cm shorter than x.

∴R is not symmetric.

Now, let (x,y),(y,z)∈R

⇒ x is exactly 7cm taller than y and y is exactly 7cm taller thanz.

⇒ x is exactly 14 taller than z.

∴(x,z)∈  R

∴R is not transitive.

Hence, R is neither reflexive, nor symmetric, nor transitive.