Write down the negation of the following statements:
1. ∀x ∈z, p(x) → q(x)
2. ∃x ∈z such that q(x) ∧∼ r(x)
3. ∃x ∈z such that p(x) → s(x)

Which of the following statements is true? a. the irrational number system is not closed under multiplication, because the product of two irrational numbers is always a rational number. b. the irrational number system is not closed under multiplication, because the product of two irrational numbers is not always an irrational number. c. the irrational number system is closed under multiplication, because the product of two irrational numbers is always an irrational number. d. the irrational number system is closed under multiplication, because the product of two irrational numbers is always a rational numbers. reset submit