Union
$$A \cup B =$$
{ avoidant, charity, collaborative, competitive, dependent, devotion, fasting, independent, participative, pilgrimage, prayer, purity, struggle }
Symmetric Difference
$$A \ominus B =$$
{ avoidant, charity, collaborative, competitive, dependent, devotion, fasting, independent, participative, pilgrimage, prayer, purity, struggle }
Cartesian Product
$$A \times B =$$
{ (charity, avoidant),
(charity, collaborative),
(charity, competitive),
(charity, dependent),
(charity, independent),
(charity, participative),
(devotion, avoidant),
(devotion, collaborative),
(devotion, competitive),
(devotion, dependent),
(devotion, independent),
(devotion, participative),
(fasting, avoidant),
(fasting, collaborative),
(fasting, competitive),
(fasting, dependent),
(fasting, independent),
(fasting, participative),
(pilgrimage, avoidant),
(pilgrimage, collaborative),
(pilgrimage, competitive),
(pilgrimage, dependent),
(pilgrimage, independent),
(pilgrimage, participative),
(prayer, avoidant),
(prayer, collaborative),
(prayer, competitive),
(prayer, dependent),
(prayer, independent),
(prayer, participative),
(purity, avoidant),
(purity, collaborative),
(purity, competitive),
(purity, dependent),
(purity, independent),
(purity, participative),
(struggle, avoidant),
(struggle, collaborative),
(struggle, competitive),
(struggle, dependent),
(struggle, independent),
(struggle, participative) }