CSET SUBTEST 1 QUESTIONS AND
CORRECT ANSWERS
Group---ans-✔✔A-set-of-elements-that-is
1.-Closed-(combining-any-two-elements-produces-a-third-element-still-in-that-set)-under-
one-operation
2.-Identity-Element
3.-Inverse-Element
4.-Associativity
Abelian-Group---ans-✔✔A-group-that-includes-the-commutative-property
Ring---ans-✔✔A-set-of-elements-that-is-a-group-and-is-closed-under-2-operations.
1.-Closed-under-addition-and-multiplication
2.-Associativity-of-addition-and-multiplication
3.-Commutativity-of-addition
4.-Identity-Elements-0-and-1
5.-Inverse-Element-for-addition
6.-Distributivity-of-addition-and-multiplication
Key-Difference:-No-Multiplicative-Inverse,-No-Commutative-Multiplication
Examples:-integers,-square-matrices,-polynomials-with-coefficients-in-a-ring
Field---ans-✔✔A-set-of-elements-that-is-closed-under-addition-and-multiplication
1.-Associativity-of-addition-and-multiplication
2.-Commutativity-of-addition-and-multiplication
3.-Identity-Elements-0-and-1
4.-Inverse-Elements--a-and-a^-1
5.-Distributivity-
Examples:-rational,-real,-and-complex-numbers
, Modular-Addition/Multiplication---ans-✔✔a-+-b(mod-n)-=-r
1.-n-is-the-number-of-elements-in-the-set,-including-0
2.-r-is-the-remainder-when-a-+-b-or-a*b-is-divided-by-n
3.-Only-applied-if-a-+-b-or-a*b-results-in-a-number-outside-the-given-set
4.-If-is-NOT-prime,-its-divisors-will-have-no-multiplicative-inverse
Natural-Numbers---ans-✔✔No-Decimals-or-Fractions,-must-be-greater-than-0
1,-2,-3,-4,-...
Whole-Numbers---ans-✔✔The-natural-numbers-including-0
0,-1,-2,-3,-4,-...
Integers---ans-✔✔Includes-positive-and-negative-natural-numbers.-Denoted-by-the-letter-
Z
-2,--1,-0,-1,-2,-...
Rational-Numbers---ans-✔✔Any-number-that-can-be-represented-as-a-fraction-or-
decimal.-If-a-decimal,-then-it-must-either-terminate-or-repeat.-Denoted-by-the-letter-Q
4.32,-3/4,-1.3333....
Irrational-Numbers---ans-✔✔Numbers-that-cannot-be-expressed-as-fraction.-A-decimal-
number-that-never-ends-and-does-not-repeat.-Denoted-by-the-letter-I
pi
Real-Numbers---ans-✔✔Set-of-all-rational,-irrational,-integer,-whole,-and-natural-
numbers.-Denoted-by-the-letter-R
Imaginary-Numbers---ans-✔✔Denoted-by-lower-case-i,-where-i-is-the-square-root-of-
negative-1
Complex-Numbers---ans-✔✔Numbers-containing-both-a-real-and-imaginary-part.-Written-
in-the-form-a+bi,-where-a-is-real-and-bi-is-imaginary
Prime-Factorization---ans-✔✔Any-non-prime-number-can-be-written-as-a-product-of-prime-
numbers.
Complex-Conjugate---ans-✔✔A-complex-number-with-the-sign-of-the-imaginary-portion-
switched.-
e.g.-a+bi-and-a-bi-are-complex-conjugates
CORRECT ANSWERS
Group---ans-✔✔A-set-of-elements-that-is
1.-Closed-(combining-any-two-elements-produces-a-third-element-still-in-that-set)-under-
one-operation
2.-Identity-Element
3.-Inverse-Element
4.-Associativity
Abelian-Group---ans-✔✔A-group-that-includes-the-commutative-property
Ring---ans-✔✔A-set-of-elements-that-is-a-group-and-is-closed-under-2-operations.
1.-Closed-under-addition-and-multiplication
2.-Associativity-of-addition-and-multiplication
3.-Commutativity-of-addition
4.-Identity-Elements-0-and-1
5.-Inverse-Element-for-addition
6.-Distributivity-of-addition-and-multiplication
Key-Difference:-No-Multiplicative-Inverse,-No-Commutative-Multiplication
Examples:-integers,-square-matrices,-polynomials-with-coefficients-in-a-ring
Field---ans-✔✔A-set-of-elements-that-is-closed-under-addition-and-multiplication
1.-Associativity-of-addition-and-multiplication
2.-Commutativity-of-addition-and-multiplication
3.-Identity-Elements-0-and-1
4.-Inverse-Elements--a-and-a^-1
5.-Distributivity-
Examples:-rational,-real,-and-complex-numbers
, Modular-Addition/Multiplication---ans-✔✔a-+-b(mod-n)-=-r
1.-n-is-the-number-of-elements-in-the-set,-including-0
2.-r-is-the-remainder-when-a-+-b-or-a*b-is-divided-by-n
3.-Only-applied-if-a-+-b-or-a*b-results-in-a-number-outside-the-given-set
4.-If-is-NOT-prime,-its-divisors-will-have-no-multiplicative-inverse
Natural-Numbers---ans-✔✔No-Decimals-or-Fractions,-must-be-greater-than-0
1,-2,-3,-4,-...
Whole-Numbers---ans-✔✔The-natural-numbers-including-0
0,-1,-2,-3,-4,-...
Integers---ans-✔✔Includes-positive-and-negative-natural-numbers.-Denoted-by-the-letter-
Z
-2,--1,-0,-1,-2,-...
Rational-Numbers---ans-✔✔Any-number-that-can-be-represented-as-a-fraction-or-
decimal.-If-a-decimal,-then-it-must-either-terminate-or-repeat.-Denoted-by-the-letter-Q
4.32,-3/4,-1.3333....
Irrational-Numbers---ans-✔✔Numbers-that-cannot-be-expressed-as-fraction.-A-decimal-
number-that-never-ends-and-does-not-repeat.-Denoted-by-the-letter-I
pi
Real-Numbers---ans-✔✔Set-of-all-rational,-irrational,-integer,-whole,-and-natural-
numbers.-Denoted-by-the-letter-R
Imaginary-Numbers---ans-✔✔Denoted-by-lower-case-i,-where-i-is-the-square-root-of-
negative-1
Complex-Numbers---ans-✔✔Numbers-containing-both-a-real-and-imaginary-part.-Written-
in-the-form-a+bi,-where-a-is-real-and-bi-is-imaginary
Prime-Factorization---ans-✔✔Any-non-prime-number-can-be-written-as-a-product-of-prime-
numbers.
Complex-Conjugate---ans-✔✔A-complex-number-with-the-sign-of-the-imaginary-portion-
switched.-
e.g.-a+bi-and-a-bi-are-complex-conjugates
