Show that the operation which is defined by

is NOT a binary operation on N.

**Q. 1 Solution:**

When x + y is less than xy, then x + y - xy does not belong to N.

So it is not a binary operation on N.

Show that the set fbafc6b9-c88d-49e2-8d4c-bf3d558f731c-image.png is a group under the binary operation of multiplication.

**Q. 2 Solution:**

ec6445ed-0169-4c89-80d0-895262fc6049-image.png

93643cde-f437-47ce-bd11-280b9c654e27-image.png

Hence G ={1,-1} is a group , since all the axioms of the group are satisfied on G={1,-1} with respect to binary operation multiplication.

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