8 21 Abstract alg Structure
Sets w some
operations
sets collection of
efforts
a
What is not
EA Y A
element set
Def A subset of a set A is a set whose
elements are all in A
IBIII
motto 1.2.3
4
faurealnumber.se
344
01
, aconscates cdidates
EI 1 0 empty set
2 IR Z M Kif matrix
iii Hilarion
cardinality
Property the number of elements
main focus
finite sets
Gintertesett Ignore for areas
Def AUB
Tionintersett TEA or EB union
AND XEA and XEB intersection
EX S a b c
T c die
SUT a b c d e
SAT c
,proof AUB BUA
AAB BMA
To prove A B
A C B XEA NEB A B
A B
BE A XEB XEA B CA
1 AUB BUA
PS XEAUB XEB or XEA XEA or XEB
EBUA
50
AUBEBUA
similarly
BUA AUB
50
AUB BUA
, 8 23
Ex
Prove AUB NC ANC U BAC
ANC U BAC
Proof want to show
AUB NC ANC U Bre
E AUB NC
XE AUB and EC
XE A or B and XEC
Now EA and C XE B and C
or
XE ANC U BNC
ANC ULBAC AUB NC
XeArc U BAC
XE A and C or e B and C
EC and XEA of XEB
ᵗA0B
I Au
Sets construct new sets
subset add restrictions
AUB AAB A
A B AND
Cartesian Prod
A B
_gfg
aeA beB
Lay
Sets w some
operations
sets collection of
efforts
a
What is not
EA Y A
element set
Def A subset of a set A is a set whose
elements are all in A
IBIII
motto 1.2.3
4
faurealnumber.se
344
01
, aconscates cdidates
EI 1 0 empty set
2 IR Z M Kif matrix
iii Hilarion
cardinality
Property the number of elements
main focus
finite sets
Gintertesett Ignore for areas
Def AUB
Tionintersett TEA or EB union
AND XEA and XEB intersection
EX S a b c
T c die
SUT a b c d e
SAT c
,proof AUB BUA
AAB BMA
To prove A B
A C B XEA NEB A B
A B
BE A XEB XEA B CA
1 AUB BUA
PS XEAUB XEB or XEA XEA or XEB
EBUA
50
AUBEBUA
similarly
BUA AUB
50
AUB BUA
, 8 23
Ex
Prove AUB NC ANC U BAC
ANC U BAC
Proof want to show
AUB NC ANC U Bre
E AUB NC
XE AUB and EC
XE A or B and XEC
Now EA and C XE B and C
or
XE ANC U BNC
ANC ULBAC AUB NC
XeArc U BAC
XE A and C or e B and C
EC and XEA of XEB
ᵗA0B
I Au
Sets construct new sets
subset add restrictions
AUB AAB A
A B AND
Cartesian Prod
A B
_gfg
aeA beB
Lay
