Problem 4 Let V = P₁ (R). Let W₁ = {k(x + 1) | k ≤ R}, and let W₂ = R. Prove that W₁ + W₂ = V.

5. Let u = [4] and v= [2] find a and b such that au+bv = 0 [8]

prove the following. (∀x,y)(x < y → x2 < y2). if one number is smaller than another number, then its square is smaller than that number too.

2 4. Consider the following formulas: (a). [(VxPx) v (VxRx)]-Vx(Px v Rx) and (b). [Vx(Px v Rx)] → [(VxPx)v (VxRx)] Which one is always true in any model? Give a model where the other one is false.