Question

Let X = { prime factors of 21156 } and Y ={ Prime factors of 93310 }. Find Boolean sum

of X and Y. Show that DeMorgan’s law are applicable on these sets.

Answer 1

parime factor of 21156 = 2X2 X3x41x43 n { prime factor of 21.15 > {2, 2, 3, 44,43} porime factor of 93310 = 2X5X7X34X43 Y = { prime factor of 9 3310} > { 2, 5, 7, 31,43} let set of all prime number = P = { 2, 3, 5, 7, 11, 13,17,19,23,29,31, 37,44,43,47 ----} "Booleans um of xfY > (XUY) = {2,3,5,7,31,41,433 Ang for De Morgan's lawo gst (Xur) = x'ny' 2nd (Xny) = xiure - W

IDP (XUY]' = x'ny' ( XUY= { 2, 3, 5, 1, 1, 1, 13 (XU y)' = - (X (Y) (a hore pa set of all prime number) [X UY)'= 11, 13, 14, 15 23, 29, 33, 47, --- X'z P-X X'={ 5,7,11,13,17,19,23,29, 31,37,47 Y' P-Y Y' = { 3,11,13,18,19, 23,29, 37,44,47___} x'ny' = { 11, 13, 17, 19, 23, 29, 37, 47 - from eq. (11 4 W (XUY) = xhyn proved

&xny]' X'uy' exny) = {2,43} (any)" = P-XnY) 3) (x nye = { 3,5,9,14,13,17,19,23,29, 31, 32, 42,47----} ♡ Similarly X'> {5,7,11,13,17,19,23,29,34,39,47 ----3 Y'= {3,11,13,17,19,23,29,37,44,47 ----} x'uy's {3,5,7,11,13,17, 19,23,29,31,37,49,47 ---- D (vil from eq- 4 any) = x'uy' proved