# GATE Papers >> EEE >> 2019 >> Question No 9

Question No. 9

Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The product of elements having minimum and maximum values in the set Z is ____.

##### Answer : (D) 3/8

Solution of Question No 9 of GATE 2019 EEE Paper

Given two sets

X = {1,2,3} & Y = {2,3,4}

$\therefore\mathrm Z=\left\{\frac12,\frac13,\frac14,\frac22,\frac23,\frac24,\frac32,\frac33,\frac34\right\}\rightarrow$ set of all possible fraction;

where the numberators belongs to set X and the denominators belongs to set Y.

$\Rightarrow\mathrm Z=\left\{\frac1{\begin{array}{c}4\\\downarrow\\\begin{array}{c}0.25\\\mathrm{Minimum}\end{array}\end{array}}\;\;\;\;\;,\frac13,\frac12,\frac24,\frac23,\frac34,\frac22,\frac33,\;\;\;\;\;\frac3{\begin{array}{c}2\\\downarrow\\1.5\\\mathrm{Maximum}\end{array}}\right\}$

$\therefore$        The required product $=\frac14\times\frac32=\frac38$