If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, Find :
`A cap B`
`A cap C`
`B cap D`
`C cap D`.

Answer

`XuuY={(x, y):x^(2)+y^(2)le1or0lexle1and-1leyle1}`
`XnnY={(x,y):x^(2)+y^(2)le1andxge0}`

Explanation

`X={(x,y):x^(2)+y^(2)le1}`
`Y={(x,y):0lexle1-1leyle1}`
`XuuY={(x,y):x^(2)+y^(2)le1or0lexle1and-1leyle1}`
`XnnY={(x,y):x^(2)+y^(2)le1andxge0}`