11. Let = {(, ) |2 + 5 = 1} a. Is S a function? justify b. Is a function? justify 1 12. Let = (, ) | = 2 { }, = (, ) | = 3 { } Show with an example that ST) 1 1 1 13. Let f: R R,f(x)= +1 <1 { 1 } accept that f is a function. show not one to one. 14. let g: r r,g(x) =2>1 } Show (with an example) that there is b R such that g(a) b, for all a R 15. Let S={(x,y)ZZ|2x+4y=6z some zZ}, let T ={(x,yZZ|5x+1=6c some cZ} Accept that S and T are equivalence relations. Let [2] be the equivalence class of 2 according to S and let < 2 > be the equivalence class of 2 according to T. Show that [2] < 2 >