Question 1: 40 Marks Convert the following English sentences to First Order Logic You can fool some of the people all of the time. You can fool all of the people some of the time. All purple mushrooms are poisonous. No purple mushroom is poisonous. There are exactly two purple mushrooms. X is above Y if X is on directly on top of Y or else there is a pile of one or more other objects directly on top of one another starting with X and ending with Y. Gold/silver armaments are precious Question 2: 30 Marks Which of these formulas is correct, give detailed explanation to your achoice of answer. a. Every teacher is liked by some student 1. Vx[teacher(x) + 3y[student(y) like(y,x)] 2. Vx[teacher(x) + 3y[student(y) A likes(y,x)] 3. 3yVx[teacher(x) + (student(y) Alikes(y,x] b. Some boys in the class are taller than all the girls 1. 3x[boy(x( Vy[girl(y) A taller (x.y)]] 2. x[boy(x) A Vy[girl(y) A taller(x, y)]] 3. 3x[bou(x) Vy[girl(y) taller(x, y)]] 4. 3x[boy(x) A Vy[girl(y) taller(x,y]]