Question

if A{x:x is a natural number less than 6} B{x:x is a prime number which is divisor of 60} C{ x:x is an odd natural number less than 10}D{x;x is an even natural number which is divisor of 48 then find AUB,BUC,A-D,D-B​

Answer 1

A U B = {1, 2, 3, 4, 5}

B U C = {1, 2, 3, 5, 7, 9}

D - A = {6, 8, 12, 16, 24}

D - B = {4, 6, 8, 12, 16, 24}

Step-by-step explanation:

A = {x | x ∈ N, x < 6 } = {1, 2, 3, 4, 5}

B = {x| x is a prime number which is divisor of 60} = {2, 3, 5}

Here, B ⊂ A,

Therefore A U B = A = {1, 2, 3, 4, 5}

C = { x | x is an odd natural number, x < 10}

= {1, 3, 5, 7, 9}

So, B U C = {1, 2, 3, 5, 7, 9}

D = {x | x is an even natural number which is divisor of 48} = { 2, 4, 6, 8, 12, 16, 24}

D - A means x ∈ D and x ∉ A

Therefore, D - A = {6, 8, 12, 16, 24}

D - B means x ∈ D and x ∉ B

Therefore, D - B = {4, 6, 8, 12, 16, 24}