Question

ε = {x: 2 ≤ x ≤30, x is an integer}, M = {even numbers}, P = {prime numbers}, T = {odd numbers} Find:

(i) P∪(M∩T),
(ii) P’U(M∩T’)

Answer 1

Given 1 ) U = { x:2 ≤ x ≤ 30, x is an integer }

U = {2,3,...,28,29,30}

2) M = { Even numbers },

M = { 2,4,8,10,12,...,28,30}

3) P = { Prime numbers },

P = { 2,3,5,7,11,13,17,19,23,29}

4) T = { Odd numbers },

T = { 3,5,7,...,27,29}

Now,

I) MUP = { 2,4,8,10,12,...,28,30}U{ 2,3,5,7,11,13,17,19,23,29}

= { 2,3,4,5,7,8,10,11,13,14,16,17,18,19,20,22,23,24,26,28,29}

ii) M - T = { 2,4,8,10,12,...,28,30} - { 3,5,7,...,27,29}

= { 2,4,8,10,12,...,28,30}= M

iii) PU(MnT) = { 2,3,5,7,11,13,17,19,23,29}U( { 2,4,8,10,12,...,28,30} n { 3,5,7,...,27,29})

= { 2,3,5,7,11,13,17,19,23,29}U { }

= { 2,3,5,7,11,13,17,19,23,29}

= P

2) P' = U - P

= {2,3,...,28,29,30} - { 2,3,5,7,11,13,17,19,23,29}

= { 4,6,8,9,10,14,15,16,18,20,21,22,24,25,26,27,28,30}

T' = U - T

= {2,3,...,28,29,30} - { 3,5,7,...,27,29}

= { 2,4,6,8,...,28,30}

MUT' = { 2,4,8,10,12,...,28,30} U { 2,4,6,8,...,28,30}

= { 2,4,6,8,...,28,30}

Now,

iv) P'U( M UT')= { 4,6,8,9,10,14,15,16,18,20,21,22,24,25,26,27,28,30} U { 2,4,6,8,...,28,30}

= { 2,4,6,8,...,28,30}

•••♪