Maths : what is meant by square free ?

Question

D₃₀={1,2,3,5,6,10,15,30}

because D₃₀ is square free so it is boolean algebra and every  boolean algebra is distributed and complemented also

here square free means no divisor of 30 is square ?

Answer 1

A positive integer n is said to be square free if Dn have no element which are perfect square(except 1).

For example [D27,/]

D27={1,3,9,27}

But  here 3 perfect square is 9 which is present in D27.Hence it is not square free integer.

In your case, D30 will be square free.

Comments

and if it is like {1,3,27} then it k ?

---

it will be square free in this case