If a,b,c are respectively the sums of p,q,r terms of an A.P., prove that `a/p(q-r)+b/q(r-p)+c/r(p-q)=0`

If a,b,c are respectively the p^(th),q^(th),r^(th) terms of an A.P.,then prove that a(q-r)+b(r-p)+c(p-q)=0

If x,y,z are positive and are the pth, qth and rth terms of a G.P. then prove that |[logx,p,1],[logy,q,1],[logz,r,1]|=0

If a^2,b^2,c^2 are in A.P. prove that 1/(b+c),1/(c+a),1/(a+b) are in A.P.

If a^2,b^2,c^2 being A.P prove that cotA,cotB,cotC are also In A.P.

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious "," You will receive a promotion" Translate |r vv (~~p)| rarr ~~q statements into English language.

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ",and " you will receive a promotion " Translate (p vv q) rarr r statements into English language .

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate ~~(p vv q) rarr~~r statements into English language .

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ","you will receive a promotion" Translate p^^q^^r statements into English language.

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate ~~r rarr ~~p statements into English language .