Tour:Objective evaluator two (beginners)

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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 $suchthat<math>AB=BA$, 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 $g(A\cup B)=gA\cup gB$.

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