Prove by truth tables that `-(p^^q) =- pvv-q`

Write the truth table of OR gate.

Write the truth table of AND gate.

If pth term of a G.P. is P and its qth term is Q, prove that the nth term is ((P^(n-q))/(Q^(n-p)))^(1/(p-q)) .

Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove that a/p(q-r) +b/q(r-p) + c/r(p-q)=0 .

If two distinct chords, drawn from the point (p, q) on the circle x^2+y^2=p x+q y (where p q!=q) are bisected by the x-axis, then p^2=q^2 (b) p^2=8q^2 p^2 8q^2

The locus of the orthocentre of the triangle formed by the lines : (1 + p)x - py + p(1+ p) = 0, (1 + q)x- qy + q(1+ q) = 0, and y = 0 , where p ne q , is :

Find the product: (p+3q) (3p-q)

If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y^(r-p).z^(p-q) =1 .