13. If s(r)=a + at+at++ a, . Then prove that lim s(r)=f (a)

Let R and S be two relations on a set A. If (i) R and S are both symmetric on A prove that R cup S and R cup S are also symmetric on A

If p + r = 2q and 1/q + 1/s = 2/r , then prove that p : q = r : s .

Let R and S be two relations on a set A. If (ii) R is reflexive and S is any relation prove that R cup S is reflexive

If R and S are relations on a set A , then prove the following: R and S are symmetric =>RnnS and RuuS are symmetric (ii) R is reflexive and S is any relation =>RuuS is reflexive.

If the equations of two circles, whose radii are r and R respectively, be S = 0 and S' = 0, then prove that the circles S/r+-(S')/R=0 will intersect orthogonally

If R and S are relations on a set A , then prove the following : (i) R and S are symmetric RnnS and RuuS are symmetric, (ii) R is reflexive and S is any relation RuuS is reflexive.

If R and S are relations on a set A, then prove the following: R and S are symmetric $R nn S and R uu S are symmetric R is reflexive and S is any relation hat varphi R uu S is reflexive.

If R and S are relations on a set A, then prove the following: R and S are symmetric rArr R nn S and R uu S are symmetric (ii) R is reflexive and S is any relation rArr R uu S is reflexive.

If R and S are relations on a set A , then prove the following : R and S are symmetric RnnS and RuuS are symmetric R is reflexive and S is any relation RuuS is reflexive.

If r lt s le n " then prove that " ^(n)P_(s) " is divisible by "^(n)P_(r).