Let A={1,2,3,4,5,6,7,8}A={1,2,3,4,5 ,6,7,8}. Define a relation ∼∼ on AA by a∼ba∼b if and only if 33 divides a−ba−b for all a, b∈Aa, b∈A.  1. Find all the pairs (a, b)∈A×A(a, b)∈A×A such that a∼ba∼b. 2. Show that ∼∼ is an equivalence relation on AA. 3.  Find the equivalence classes [2][2] and [3][3].​

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