Question

if x∈{2,3,4} and y∈{4,6,9,10}, form the set of all ordered pairs (x,y) such that x is a factor of y

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

x∈{2,3,4} and y∈{4,6,9,10}

TO find the set of all ordered pairs (x,y) such that x is a factor of y

CALCULATION

Let R be the required Set.

Then

$\sf{ R = \{ \: (x, y) : x \: is \: a \: factor \: of \: y\: \}}$

Here

$\sf{2 \: is \: a \: factor \: of \: 4 \: \: implies \: (2,4) \in R}$

$\sf{2 \: is \: a \: factor \: of \: 6 \: \: implies \: (2,6) \in R}$

$\sf{2 \: is \: a \: factor \: of \: 10 \: \: implies \: (2,10) \in R}$

$\sf{3 \: is \: a \: factor \: of \: 6 \: \: implies \: (3,6) \in R}$

$\sf{3 \: is \: a \: factor \: of \: 9\: \: implies \: (3,9) \in R}$

$\sf{4 \: is \: a \: factor \: of \: 4 \: \: implies \: (4,4) \in R}$

Hence

$\sf{R = \{ (2,4),(2,6),(2,10),(3,6),(3,9),(4,4) \}}$

RESULT

Hence the required Set is

$\sf{= \{ (2,4),(2,6),(2,10),(3,6),(3,9),(4,4) \}}$

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Answer 2

Answer:

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