Let `X={2,3,4,5}andY={7,9,11,13,15,17}`. Define a relation f from X to – InterviewSolution

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1.	Let `X={2,3,4,5}andY={7,9,11,13,15,17}`. Define a relation f from X to Y by: `f={(x,y):x""inX,yinYandy=2x+3}`. (i) Write in roster form. (ii) Find dom (f) and range (f). (iii) Show that f is a function from X to Y.
Answer» Here `X={2,3,4,5}andY=2x+3`. Now, `x=2impliesy=(2xx2+3)=7`, `x=3impliesy=(2xx3+3)=9`, `x=4impliesy=(2xx4+3)=11`, `x=5impliesy=(2xx5+3)=13` (i) `:.f={(2,7),(3,9),(4,11),(5,13)}`. (ii) Clearly , dom `(f)={2,3,4,5}` and range `(f)={7,9,11,13}subY`. (iii) It is clear that no two distinct ordered pairs in f have the same first coordinate. `:. f is function from X to Y.

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