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Among the options below there are 7 different partitions of the set $A = \lbrace 0, 1, 2, \dots , 13 \rbrace$ . List them on the right according to the number of equivalence classes that each partition induces. Here, $Z_k= \lbrace 0, 1, \ldots, k-1\rbrace$ .

Choose from these collections of sets

{0},{1},{2},...{12},{13}
{0,1,2,...,8},{9,10,...,13}
$Z_1,Z_2,Z_3,Z_4,Z_5,$
$Z_6,Z_7,...,Z_{12},Z_{13}$
{even integers less than 13},
{odd integers less than 13},{13}
$S_0 =$ {0}, $S_1 =$ {3,6,9}, $S_2 =$ {1,4,7,10}, $S_3 =$ {2,5,8}, $A - S_0 - S_1 - S_2 - S_3$
{even positive integers less than 13},
{odd positive integers less than 13},{0,13}
{1},{2},...{12},{13},{14}
{even positive integers less than 13},
{odd positive integers less than 13},{0},{13}
{0,13},{1,12},{2,11},{3,10},...,{6,7}
{0,1,2,...,13}
{1,2,...,5}, {6,8,...,12}

Partitions of S by increasing number of classes.

Choose from these collections of sets

{0},{1},{2},...{12},{13}
{0,1,2,...,8},{9,10,...,13}
$Z_1,Z_2,Z_3,Z_4,Z_5,$
$Z_6,Z_7,...,Z_{12},Z_{13}$
{even integers less than 13},
{odd integers less than 13},{13}
$S_0 =$ {0}, $S_1 =$ {3,6,9}, $S_2 =$ {1,4,7,10}, $S_3 =$ {2,5,8}, $A - S_0 - S_1 - S_2 - S_3$
{even positive integers less than 13},
{odd positive integers less than 13},{0,13}
{1},{2},...{12},{13},{14}
{even positive integers less than 13},
{odd positive integers less than 13},{0},{13}
{0,13},{1,12},{2,11},{3,10},...,{6,7}
{0,1,2,...,13}
{1,2,...,5}, {6,8,...,12}

Partitions of S by increasing number of classes.