Let A = {6, 7, 8, 10, 12, 13} and B = {5, 7, 9, 11, 13, 15} and the relation R from A to B means, "is greater than". Find R. Also, draw a suitable diagram to represent this relation.

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Solution

$A = {6, 7, 8, 10, 12, 13}$
$B = {5, 7, 9, 11, 13, 15}$
R is the set of all ordered pairs whose 1^st component is greater than the second component.
$∴ R = {(6, 5), (7, 5), (8, 5), (9, 5), (10, 5), (12, 5), (13, 5), (8, 7), (10, 7), (12, 7), (13, 7), (10, 9), (12, 9), (13, 9), (12, 11), (13, 11)}$

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U = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, A = {3, 4, 5, 6, 9}, B = {3, 7, 9, 5}

C = {6, 8, 10, 12, 7}

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Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

A survey was conducted to identify vegetarians in a group of people. Find the mode of the data.

Group	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$	$13 - 15$	$15 - 17$
Frequency	$6$	$7$	$3$	$7$	$12$	$9$

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