c) This question involves Predicate Calculus. Suppose you are playing a board game that involves using counters with from three to seven sides, which can be red, blue or green. Your allocation of counters for the current game is shown below. Triangle: 6 red, 4 green, blue Rectangle: 3 red, green, blue OOOOD Pentagon: 1 red, 1 green, o blue Hexagon: 0 red, green, 8 blue Heptagon: red, green, blue. For each of the following formulas i-v, you should write out the literal meaning English, express it in ordinary language and explain whether it is true or false in this setting- For example: 3x(Rectangle(x) Red(x)) Literal meaning: There is no x, such that x is a rectangle and x is red. Ordinary language: No rectangles are red or there are no red rectangles. True or false? False: there are in fact three red rectangles. 4 i. ii. iii. iv. V. Vx(Triangle(x) (Red(x) v Green(x))) ax(Rectangle(x) (Green(x)) ax(Pentagon(x (Red(x) Green(x))) Vx(Hexagon(x) A Blue(x)) Vx(Heptagon(x) - Blue(x)) Finally, express the following statements as formulas of Predicate Calculus and explain whether they are true or false. You should explain the intended meanings of any constant terms or predicates you use. vi vii. All counters with an even number of sides are red or blue. No counters with an odd number sides are blue