I have two questions about the properties of binary set operations that I am having difficulty arriving at answers that I completely trust (though I am sure they are not difficult questions). Here they are:

1. Of the 16 binary operations on subsets satisfy the idempotent law? -Clearly the answer is at least 2, but binary operations P and Q are idempotent as well, correct?

2. Under how many of the 16 binary operations on the subsets of a set do the latter form a group? -I am not really sure how to solve this question.

1. Of the 16 binary operations on subsets satisfy the idempotent law? -Clearly the answer is at least 2, but binary operations P and Q are idempotent as well, correct?

2. Under how many of the 16 binary operations on the subsets of a set do the latter form a group? -I am not really sure how to solve this question.