Question

let a relation R be defined as R=(A,B) I A is an ancestor of B )
state whether true or false : R is an symmetric

Answer 1

Answer:

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Answer 2

relation is not symmetric

Given

• R={(A,B) I A is an ancestor of B )}

To find

• If R is a symmetric, true or false

Solution

we are provided with a relation are under asked to judge if the given statement that is R is symmetric is true or false.

for a relation to be symmetric we know that condition,

if (a,b) belongs to R then (b,a) should also belong to R.

the given relation,

(A,B) I A is an ancestor of B )

let us consider two points in accordance with the relation, ie,

(a,b) belong to R then,

a is an ancestor of b ,

this assumption immediately ponits to the conclusion that b cannot be ancestor of a.

therefore, (b,a) cannot belong to the relation R .

Thus, (a,b) belongs to R and (b,a) does not belong to R

Therefore, we conclude that the given relation is not symmetric