" If Prove that "{{a},{a,b}}={{c},{c,d}}" iff "a=c" and "b=d

Prove that [a xx b,a xx c,d]=(a*d)[a,b,c]

If a ,b ,c ,d are in G.P., prove that a+b,b+c ,c+d are also in G.P.

If a

If a,b,c and d are in H.P.,then prove that (b+c+d)/a,(c+d+a)/b,(d+a+b)/c and (a+b+c)/d, are in A.P.

If a + c = b e and 1/b + 1/d = e/c , Prove that : a,b,c and d are in proportion.

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

Is R an equivalence relation in the set NxxN which is defined as (i) (a,b)R(c,d) iff a+d=b+c (ii) (a,b)R(c,d) iff ad=bc for all (a,b),(c,d) in NxxN ?

If (a+b)/(b+c) = (c +d)/(d + a) , that prove that c = a " or, " a + b + c + d = 0 .