8. Rewrite the following statements using the symbol V and the variable x. a) Every real number is positive, negative, or zero. b) All students are eager to learn. 9. Rewrite the following statements using the symbol 3 and the variable .x. a) Some computers are inexpensive. b) Some people enjoy solving math puzzles. 10. What is the hidden quantifier (For all or There exists) in each of the following statements? a) If a triangle is equilateral, then it is equiangular. b) sinx + cosx = 1 c) sin x= 1 11. Let the domain D of x be all students in a certain college. Let F(x) be "x attends football games" and let B(x) be "x attends basketball games" Rewrite the following statements without using quantifiers, variables, or other symbols. a) 3x E D such that F(x)^ B(x) b) VxED, F(x) v B(x) c) 3x D such that ~ (F(x) v B(x) 1. Write the negation symbolically: vy D,P(y) 2. Write the negation symbolically: 3 g G such that R(g) 3. Write the negation symbolically: Vx, P(x) Q(x) 4. Write the negation in words: All prime numbers are odd. 5. Write the negation in words: There is at least one journalism major in the class. 6. Write the negation in words: For all pairs of real numbers (x,y), if x and y are irrational, then the product xy is irrational. 7. Write in IF-THEN form: Earning a C in a prerequisite course is sufficient to register for the following course. 8. Write in IF-THEN form: Being at least 35 years old is a necessary condition for being president of the United States. 9. Write the inverse of the following statement symbolically: Vx ED, ~ P(x) Q(x) 10. Write the contrapositive of the following statement in words: For all US citizens x.if x is younger than 18 years, then x cannot vote.