Boolean Algebra

Question

Which of the following is not a boolean Algebra

(a) D40        (b) D66

(c) D210       (d) D646

Answer 1

Ans will be A

Theorem  

Let n=p1p2…pk, where the pi are distinct primes.

The Dn is aBoolean algebra.

choice A) n=40  =2x2x2x5  so it is not a  boolean algebra ( 2 is repeating) Hence the ans

B) n=66 =2x3x11  so it is boolean algebra (all are distinct)

C)n=210=2x3x5x7 so it is boolean algebra (all are distinct)

D) n=646 =2x323 so it is boolean algebra (all are distinct)