question archive 11) Let S={(x,y)Q×IR|2x+5y=1} a
11) Let S={(x,y)Q×IR|2x+5y=1} a
Subject:MathPrice: Bought3
11) Let S={(x,y)Q×IR|2x+5y=1} a. Is S a function? justify b. Is ???? a function? justify −1 12. Let S={(x,y)∈IR×IR|y=???? },T ={(x,y)∈IR×IR|y= } 2 ???? 3 Show with an example that ST ) ?= −1 ???? −1 ???? −1 13. Let f:IR→IR,f(x)= {???? + 1 ???????? ???? < 1;} {???? − 1 ???????? ???? ≥ 1.} Accept that f is a function. Show that f is not one to one. 14. Let g:IR→IR,g(x)= {2 − ???? ???????? ???? ≤ 1;} {1 − ???? ???????? ???? > 1.} Show (with an example) that there is b ∈ IR such that g(a) ?= b, for all a ∈ IR 15. Let S={(x,y)∈Z×Z|2x+4y=6z some z∈Z}, let T ={(x,y∈Z×Z|5x+1=6c some c∈Z} 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 >
