Tour:Objective evaluator two (beginners): Difference between revisions
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# 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>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 | # 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</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>. | # 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>. | ||
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target = beginners| | target = beginners| | ||
secnum = four| | secnum = four| | ||
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next secnum = three| | next secnum = three| | ||
next = Introduction three (beginners)| | next = Introduction three (beginners)| | ||
previous = Inquiry problems two (beginners)}} | previous = Inquiry problems two (beginners)}} | ||
Latest 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)
PREVIOUS: Inquiry problems two (beginners)| UP: Introduction four | NEXT: Introduction three (beginners)
NEXT SECTION Objective evaluator: Objective evaluator three
General instructions for the tour | Pedagogical notes for the tour | Pedagogical notes for this part
True/false questions
These questions should take at most three minutes per question.
- If is a nonempty subset of a group and is closed under the group multiplication, then is a subgroup.
- If and are subsets of a group such that , then for all .
- If are elements of a group such that , then commutes with .
- If are elements of a group such that , then .
- For subsets of a group , and , we have .
- For subsets of a group and , we have .
- For subsets of a monoid and , we have .
- For subsets of a monoid and , we have .
This page is a Objective evaluator page, part of the Groupprops guided tour for beginners (Jump to beginning of tour)
PREVIOUS: Inquiry problems two (beginners)| UP: Introduction four | NEXT: Introduction three (beginners)
NEXT SECTION Objective evaluator: Objective evaluator three
General instructions for the tour | Pedagogical notes for the tour | Pedagogical notes for this part