Question

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

Answer 1

Given: ε = {x: 2≤ x ≤30}  , M = {even numbers} , P = {prime numbers} , T = {odd numbers}

To find:   1. M U P    2. M - T   3. P ∪ (M ⋂ T)

Solution:

• Now we have given:

                       ε = {x: 2≤ x ≤30}

• So:

                       M = { even numbers } = { 2 , 4 , 6 , 8 ............... 28 , 30 }

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

                        T = {odd numbers} = { 3 ,   5 ,   7 , 9.................. 27 , 29 }

• Now we have:

                       1. M ∪ P = { 2, 3, 4, 5, 6, 7, 8, 10, 11,  12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30 }

                        2. M - T =  n(M) - n(T)

                       M - T = 15 - 14 = 1

                        3. P ∪ (M ⋂ T)

                       Now, M ∩ T = 0

                        P ∪ (M ∩ T ) =  P ∪ (∅) =  {2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }

Answer:

                So M ∪ P = { 2, 3, 4, 5, 6, 7, 8, 10, 11,  12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30 },  M - T =  1 and  P ∪ (M ∩ T ) =  {2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }