Question 1126619

all prime numbers between 1 and 100

A={2 ,3 , 5 ,7 , 11,13 , 17 , 19 , 23 , 29, 31 , 37 , 41, 43 ,47 ,53 ,59 , 61 ,67,71 }... (25 primes)

B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100}


( A U B ) The union of two sets is the set of elements contained in both sets. 


( A U B )={2, 3,4,5, 6,7, 8, 10,11, 12,13, 14, 16,17, 18,19, 20, 22, 23,24, 26, 28,29, 30,31, 32, 34, 36, 37,38, 40, 41,42,43, 44, 46,47, 48, 50, 52, 53,54, 56, 58, 59,60,61, 62, 64, 66, 68, 70, 71,72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100}



C = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99}


( A U B ) ∩ C

look for the elements you can find in both (A U B) and C: the intersection of two sets is the set of elements that are common to both sets 


I will highlight elements that are common


A U B={2, {{{3}}},4,5, {{{6}}},7, 8, 10,11, {{{12}}},13, 14, 16,17, {{{18}}},19, 20, 22, 23,{{{24}}}, 26, 28,29, {{{30}}},31, 32, 34, {{{36}}}, 37,38, 40, 41,{{{42}}},43, 44, 46,47, {{{48}}}, 50, 52, 53,54, 56, 58, 59,{{{60}}},61, 62, 64, {{{66}}}, 68, 70, 71,{{{72}}}, 74, 76, {{{78}}}, 80, 82, {{{84}}}, 86, 88, {{{90}}}, 92, 94, {{{96}}}, 98, 100} 


C= { {{{3}}}, {{{6}}}, 9, {{{12}}}, 15, {{{18}}}, 21,{{{ 24}}}, 27, {{{30}}}, 33,{{{ 36}}}, 39, {{{42}}}, 45, {{{48}}}, 51, 54, 57, {{{60}}}, 63, {{{66}}}, 69, {{{72}}}, 75, {{{78}}}, 81, {{{84}}}, 87, {{{90}}}, 93,{{{ 96}}}, 99}

so,

( A U B ) ∩ C={ {{{3}}}, {{{6}}},{{{12}}}, {{{18}}},{{{ 24}}},{{{30}}}, {{{ 36}}},{{{42}}},{{{48}}},{{{60}}},{{{66}}},{{{72}}}, {{{78}}}, {{{84}}},  {{{90}}},{{{ 96}}} }


( A U B ) ∩ C have {{{16}}} elements