(Q1)-A-State(First fundamental theorem) and Show that :(2₂0 /(10), +..) -B-Let f:( M, (Z).+-)-(M, (2).+..) be a function define by such that g vM, (2). Is f is epimorphism (02)-A- نموذجD1 (Z₁0+1010)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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E MEO r,90K/s l 36ll ZAIN IQ
zain 1Q
محمد فره. . .
>
Digi
(Q1)-A- State(First fundamental theorem ) and Show that :(2,, /(10 ), +,.) = (Z0,+10 r 19)
-B- Let f:( M, (Z),+,)-(M,(Z),+,.) be a function define by such that gt4 ) = 9.
v4 E M,(Z) . Is f is epimorphism
(Q2) -A-
() In a ring of (2,+,). Find (147)n (63) n (8)
(1) Find the following: rad. (Zo0), rad.(Z4)
(HI) Prove or disprove : the natural mapping is epimorphism function
(B) Choose and write the correct answer in each sentence a, b,cor d, with a reason.
1- let f: (7, +,)- (Q. +..) be a function such that f(n) = 2n, Vn €Z, then ker. f
(4) (0)
2-lf g: (Z,+,-) -(Z/(n),+) be a function such that g(a) = a + (n), Va €Z. then Im.g.
(b) z
(C) has no kernel
(4) (n)
(a) Z
(b) Z/(n)
(C) (n)
(d) all of them false
Transcribed Image Text:E MEO r,90K/s l 36ll ZAIN IQ zain 1Q محمد فره. . . > Digi (Q1)-A- State(First fundamental theorem ) and Show that :(2,, /(10 ), +,.) = (Z0,+10 r 19) -B- Let f:( M, (Z),+,)-(M,(Z),+,.) be a function define by such that gt4 ) = 9. v4 E M,(Z) . Is f is epimorphism (Q2) -A- () In a ring of (2,+,). Find (147)n (63) n (8) (1) Find the following: rad. (Zo0), rad.(Z4) (HI) Prove or disprove : the natural mapping is epimorphism function (B) Choose and write the correct answer in each sentence a, b,cor d, with a reason. 1- let f: (7, +,)- (Q. +..) be a function such that f(n) = 2n, Vn €Z, then ker. f (4) (0) 2-lf g: (Z,+,-) -(Z/(n),+) be a function such that g(a) = a + (n), Va €Z. then Im.g. (b) z (C) has no kernel (4) (n) (a) Z (b) Z/(n) (C) (n) (d) all of them false
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