Graded Activity 1 (Variables) Fill in the blanks using a variable or variables to rewrite the given statement. (18pts.) 1. Is there a real number whose square is -1? a. Is there a real number x such that y' = -1? b. Does there exist x such that x= -1? 2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? a. Is there an integer in such that n has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 62 b. Does there exist n such that if n is divided by 5 the remainder is 2 and if n is. divided by 6 the remainder is 3? 3. Given any two real numbers, there is a real number in between. a. Given any two real numbers a and b, there is a real number c such that c is between a and b. b. For any two real numbers a and b, such that a r. 5. The reciprocal of any positive real number is positive. a. Given any positive real number r, the reciprocal of r is positive. b. For any real number r, if'r is positive then the reciprocal of r is positive. c. If a real number r is positive, then the reciprocal of r is positive. 6. The cube root of any negative real number is negative. a. Given any negative real number s, the cube root of s is negative. b. For any real number s, if's is negative, then the cube root of s is negative. c. If a real number s is negative, then the cube root of s is negative 7. Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false. a. There are real numbers u and v with the property u + v