Tour:Objective evaluator two (beginners): Difference between revisions

Revision as of 18:20, 8 December 2008

This page is a Objective evaluator page, part of the Groupprops guided tour for beginners (Jump to beginning of tour)
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True/false questions

These questions should take at most three minutes per question.

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

This page is a {{{pagetype}}} page, part of the Groupprops guided tour for beginners (Jump to beginning of tour)
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@@ Line 12: / Line 12: @@
 # If <math>H</math> is a nonempty subset of a group <math>G</math> and <math>H</math> is closed under the group multiplication, then <math>H</math> is a subgroup.
-# If <math>A</math> and <math>B</math> are subsets of a group <math> such that <math>AB = BA</math>, then <math>ab = ba</math> for all <math>a \in A, b \in B</math>.
+# If <math>A</math> and <math>B</math> are subsets of a group such that <math>AB = BA</math>, then <math>ab = ba</math> for all <math>a \in A, b \in B</math>.
 # If <math>a,b</math> are elements of a group <math>G</math> such that <math>aba = b</math>, then <math>b^2</math> commutes with <math>a</math>.
 # If <math>a,b,c</math> are elements of a group <math>G</math> such that <math>aca = bcb</math>, then <math>a = b</math>.