Q. 12 Consider the binary operations and defined as
and . Show that ∗ is commutative but not
associative, is associative but not commutative. Further, show that ,
. [If it is so, we say that the operation ∗ distributes
over the operation ]. Does distribute over ∗? Justify your answer.
Given and is defined as
For , we have
the operation is commutative.
the operation is not associative
Let . Then we have :
Hence, operation o does not distribute over operation *.