For each of the following relations over persons state wheth

For each of the following relations over persons, state whether it is symmetric, asymmetric or neither: sister of, sibling of, parent of, ancestor of.

Solution

A.

sister of

xSy = x is sister of y

ySx = y is sister of x

xSy = ySx, cannot be always true as y can be brother of x.

Neither

B.

sibling of

xSy = x is sibling of y

ySx = y is sibling of x

xSy = ySx, this is always true

Symmetric

C.

parent of

xPy = x is parent of y

yPx = y is parent of x

xPy = yPx, this cannot be true in any case as y cannot be parent of x if x is parent of y.

Asymmetric

D.

ancestor of

xAy = x is ancestor of y

yAx = y is ancestor of x

xPy = yPx, this cannot be true in any case as y cannot be ancestor of x if x is ancestor of y.

Asymmetric