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touscours.net
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touscours.net
3. 4
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4. 6
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touscours.net
5. 7
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6. J
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touscours.net
9. O
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touscours.net
10. 3
+ , ;) - !! ' !33!** = !
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touscours.net
11. -
& →ϕ "
!4!*"!!*"!*
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• 5' "
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!! → "
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!! → % !!
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π
ψ →
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→ ' "
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→ "
1! N @
& !∈ϕ "
5 @ ϕ ' @
{ }3!Q =∈= ϕϕ "
ϕϕϕ Q*!*!* ∈−⇔=∈∀ "
ϕ ; { }3Q =⇔ ϕ "
touscours.net
12. %%
+ & ϕ ;
& ϕQ∈ " !33! ϕϕ == " 3= "
'< ' ' "
+ & - { }3Q =ϕ "
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ϕ ; "
ϕQ + "
;) ⊂ϕQ ϕQ3 ∈ "
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33"3!*"!!*" =+=+=+ λϕλϕλϕ
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ϕ ; =ϕ> "
ϕ> + "
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ϕ> $ ⋅
& ∈∈ λϕ>* "
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! > - ' +
& !∈ϕ "
5' ϕ ' + +
"
5' - ϕ ' + +
"
!ϕ + ' ϕ> !
{ }!3−
ϕ + ' ϕQ !
,
!
touscours.net
13. 4
! & '
! &
& !∈ψϕ ∈λ "
, %
!! ψϕ
ψϕ
+
→+
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"
ϕλ
ϕλ →
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B + !! ⋅+ !"
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& !∈ψϕ ∈λ "
, ∈* ∈µ
!*!"!!
!*"!!*"!
!*"!*"!*"!
ψϕµψϕ
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µψµϕµψϕ
+++=
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+++=++
!!*!""!!"
!!*""!!"
!!*"!"
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ϕλµϕλ
ϕµλϕλ
ϕµϕλ
µϕλµϕλ
+=
+=
+=
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!! ⋅+ + "
!
5 - % (
"
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"
∈* ∈µ
!*!"!!
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+=
+=
+=
+=+
!*∈ϕϕ !*∈ψψ ∈λ
!*!*
!*!*
ϕψϕψϕψψ
ϕψϕψϕϕψ
+=+
+=+
touscours.net
14. 6
!6!"!"
!4!"!"
ϕψλϕψλ
ϕψλϕλψ
=
=
;) % "
∈
!/*0
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ϕψϕψ
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+=
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!!*!!!!!*!/!*0
ϕψϕψϕψϕψ
ϕψϕψϕψψϕψψ
+=+=
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ϕψλ
ϕψλϕψλϕλψϕλψϕλψ
=
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=
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-
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→
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−
→ "
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λ
λλλ
λλλλ
+=
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!*"*"!!**"!!*"
""
"""
λ
λλλ
λλλλ
+=
−+−=+−+=
++=+=+
,
!!
"
−−
→
!33!
" →
- "
touscours.net
15. 7
4! > !
& !∈ϕ " & ϕ ; !∈−
ϕ " , -
ϕ "
( - ' (
' ' "
& ∈* ∈λ "
, - !*"!!*" −−−
+=+ ϕλϕλϕ * +)+ -
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+ ϕλϕ ϕ -
*"!!*"!!!!*"! λϕϕλϕϕϕλϕϕ +=+=+ −−−−
9
R ; "
R "
R ; % "
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→
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6!
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%%
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(
5'
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4
→
4
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!*"!*"!!*"*"*"!*" λλλλλλ +=+=+++=+
A ; - 4
C
touscours.net
16. J
B
!
4
→
!
4
4 → "
+ > ! - ∈#
#"""!
4
++
→
4#++= "
+ 6! - ∈#
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4
#++
→
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!3!"
4
→
B
!*"*"*"3!
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4
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∈∈ " % ' +
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+=
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5' @ ' "
& ∈∈ λ* "
∈∈∈∈
+=+= *** "
∈∈
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touscours.net
17. K
N @
& ∈
∈∈
+= " , -
∈⇔=⇔=⇔∈ 33!Q
>
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%
& → " , - ; - ' ( ( +
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9
; "
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E
& !∈ "
; =⇔ "
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=
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∈∈
+= =! "
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>= Q= "
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"
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# - { }3=∩
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∈ " !*= < ∈* "
∈ 3! = 3!!* = " = 3!* = "
3!* == '< ' '
"
=⊕
# - ; "
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∈∈
−+= !!! " !
%
∈∈
+
touscours.net
18. 2 -
& ;
{ }
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−=
=
=∈=
%% ∈⇔=⇔=⇔=
=−
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%
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5 ; ) ; $ "
$ >=+ "
!! $+=
5 ; { }3 ' "
5 ; { }3 ' "
! &@ !
%
& ( + " 5 @
) '
−+=
→⊕= "
touscours.net
19. O
& @ - )
!∈• "
%% - - $ >−=−= < ;
$ ; ) !
• ; B "
>= => ; ! { }3Q =
; !
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+=−=∈=
−==∈=•
E
& !∈ "
@ >=⇔
⇔ !
⇔ ' ≤ ! !
;) "
⇐ - >= "
!>Q −= !>Q += "
( + @ (
' "
{ }3=∩ ∩∈ =! −=!
3" = 3= 3≠ !
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∈∈
+= !!!! −++= "
, ∈+ ! !!!!!!! +=+=+=+
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∈∈
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! " #
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T
%
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%% "
[ ] =∈∀=∈∀⇔
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touscours.net
20. 3
9
!"""• !"""
%
⇔ ' "
• 5 - !""" @ 3=
=
λ < λ
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(
+ % "
+ ' % "
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3
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• & !""" !""" !"""9∈ "
%%
> ( µλλλ """ -
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3≠µ ' λ
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= λµ
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$ " #
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touscours.net
21. - !""" "
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=
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3=
=
λ [ ] 3=∈∀ λ (
%% 3 )
=
λ
=
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−
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6
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touscours.net