Recall that the floor of a number x = R, denoted [x], is defined as the...

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Recall that the floor of a number x = R, denoted [x], is defined as the greatest integer that is less than or equal to x. And the ceiling of x, denoted [x] is the smallest integer that is greater than or equal to x. Consider the following statement: Vx = R, [x] = [x] . (a) [1 mark] Write the negation of this statement in predicate logic. (b) [2 marks] Disprove the original statement by proving its negation in the space below. Pay attention to the structure of your proof. Recall that the floor of a number x = R, denoted [x], is defined as the greatest integer that is less than or equal to x. And the ceiling of x, denoted [x] is the smallest integer that is greater than or equal to x. Consider the following statement: Vx = R, [x] = [x] . (a) [1 mark] Write the negation of this statement in predicate logic. (b) [2 marks] Disprove the original statement by proving its negation in the space below. Pay attention to the structure of your proof.