MA103 TEST QUESTIONS WITH
100% CORRECT ANSWERS
What is an Abelian Group? - Answer-A group that is commutative
What are the subgroup axioms? - Answer-Closed
Identity
Inverse
What is Lagrange's Theorem? - Answer-If H is a subgroup of G, then the order of H
divides the order of G
What are the 3 properties of an equivalence relation? - Answer-Reflexive
Symmetric
Transitive
What is the fundamental theorem of arithmetic? - Answer-Every integer greater than or
equal to 2, can be expressed as a product of one or more prime numbers.
Why is the empty set bounded? - Answer-For instance, 1 is an upper bound for the
empty set, since the condition that all elements are less than 1 is satisfied. This is
because there is no element X of the empty set that doesn't satisfy being less than 1.
When is an element, u, said to be the least upper bound of S (or a supremum of S)? -
Answer-If:
u is an upper bound of S, and
for each upper bound x of S, it holds that u is less than x.
When is an element, l, said to be the greatest lower bound of S (or infimum of S)? -
Answer-If
l is a lower bound of S, and
for each lower y of S, it holds that l is greater than y.
If a least upper bound of a subset of the real numbers exists, is it unique? - Answer-Yes
How is the least upper bound of a set S denoted? - Answer-Sup S
How is the greatest lower bound of a set S denoted? - Answer-Inf S
If Sup S exists in S, then what is Sup S called? - Answer-A maximum of S
100% CORRECT ANSWERS
What is an Abelian Group? - Answer-A group that is commutative
What are the subgroup axioms? - Answer-Closed
Identity
Inverse
What is Lagrange's Theorem? - Answer-If H is a subgroup of G, then the order of H
divides the order of G
What are the 3 properties of an equivalence relation? - Answer-Reflexive
Symmetric
Transitive
What is the fundamental theorem of arithmetic? - Answer-Every integer greater than or
equal to 2, can be expressed as a product of one or more prime numbers.
Why is the empty set bounded? - Answer-For instance, 1 is an upper bound for the
empty set, since the condition that all elements are less than 1 is satisfied. This is
because there is no element X of the empty set that doesn't satisfy being less than 1.
When is an element, u, said to be the least upper bound of S (or a supremum of S)? -
Answer-If:
u is an upper bound of S, and
for each upper bound x of S, it holds that u is less than x.
When is an element, l, said to be the greatest lower bound of S (or infimum of S)? -
Answer-If
l is a lower bound of S, and
for each lower y of S, it holds that l is greater than y.
If a least upper bound of a subset of the real numbers exists, is it unique? - Answer-Yes
How is the least upper bound of a set S denoted? - Answer-Sup S
How is the greatest lower bound of a set S denoted? - Answer-Inf S
If Sup S exists in S, then what is Sup S called? - Answer-A maximum of S
