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Question

Let X={2,3,4,5} and Y={7,9,11,13,15,17}. Define a relation f from X to Y by:
f={(x,y):xϵX, yϵY and y=2x+3}

(i) Write f in roster form.

(ii) Find dom(f) and range (f).

(iii) Show that f is a function from X to Y.

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Solution

Let X={2,3,4,5} and Y=2x+3.

Now, x=2y=(2×2+3)=7,

x=3y=(2×3+3)=9,

x=4y=(2×4+3)=11,

x=5y=(2×5+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}Y

(iii) It is clear that no two distinct ordered pairs in f have the same first coordinate.

f is a function from X to Y.


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