Answer Happy

Let p(x, y) represent the statement, "Square z is adjacent to square y," and let q(z) represent, "Square z is white." For the purposes of this question: Squares x, y, z will be among the 3×3 grid of squares shown in the figure. • Two squares are adjacent if they share exactly one common side. (b) (c) d • Each square has a colour: either white or gray. The square marked with an r has a colour, but it has not been provided to you. You will determine its colour in part (b). (a) Write a plain-English version of the following statements: 3x y p(x, y) Aq(x)^q(y) Er Vy-q(x) ^ [p(x,y) →q(y)] b h If is it known that every gray square is adjacent to at least two white squares, then what is the colour of z? Explain why using exactly one English sentence. Prove or disprove: Vr y q(r) → [p(x, y) ^-q(y)]