Question: (1) (6 marks) Write the following below as an interval: (a) (-1,4) n (2, 3] (b) (1, oo) U (-1, 2) (c) (-3,0] - (-1,

(1) (6 marks) Write the following below as an interval: (a) (-1,4) n (2, 3] (b) (1, oo) U (-1, 2) (c) (-3,0] - (-1, -2) (2) (4 marks) Show that {r E Z| x = 6m - 5 for some integer m } = {r e Zz - 67 + 7 for some integer n} (3) (5 marks) Vr, y EZ, r Ry - 5| (1 - y). (a) Show that R is an equivalence relation. (b) Are the equivalence classes [ 21 ] , [ 103 ], and [ 1 ] the same? Is the relation R a function? (5) (5 marks) Let A = {1, 2, 3, 4, 5}. Define the relation R on the set A as a graph below. (a) Is the R reflexive? (b) Is the R symmetric? c) Is the R transitive? (d) Find the inverse of the R

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