Tour:Objective evaluator two (beginners)

True/false questions
These questions should take at most three minutes per question.


 * 1) If $$H$$ is a nonempty subset of a group $$G$$ and $$H$$ is closed under the group multiplication, then $$H$$ is a subgroup.
 * 2) If $$A$$ and $$B$$ are subsets of a group such that $$AB = BA$$, then $$ab = ba$$ for all $$a \in A, b \in B$$.
 * 3) If $$a,b$$ are elements of a group $$G$$ such that $$aba = b$$, then $$b^2$$ commutes with $$a$$.
 * 4) If $$a,b,c$$ are elements of a group $$G$$ such that $$aca = bcb$$, then $$a = b$$.
 * 5) For subsets $$A,B$$ of a group $$G$$, and $$g \in G$$, we have $$g(A \cap B) = gA \cap gB$$.
 * 6) For subsets $$A,B$$ of a group $$G$$ and $$g \in G$$, we have $$g(A \cup B) = gA \cup gB$$.
 * 7) For subsets $$A,B$$ of a monoid $$M$$ and $$g \in M$$, we have $$g(A \cap B) = gA \cap gB$$.
 * 8) For subsets $$A,B$$ of a monoid $$M$$ and $$g \in M$$, we have $$g(A \cup B) = gA \cup gB$$.