E. Let o : R+ → R* under multiplication be given by o(x) = |x|. 1. Show that is a homomorphism. 2. Find Ker(ø).

Q: Prove that Z3 x Zz is isomorphic to Zg.

A:

Q: If h:(R,+) → (R*,.) is a mapping defined by h(x)=10*, VXER, then (R,+) = (R*,.).

A:

Q: a b 2.3 Let e: (M,(R), +) → be defined by e a + d. where a,b,c,d ER (a) Prove that e is a…

A: Given that θ:M2ℝ,+→ℝ,+ is a mapping defined by θabcd=a+d where a, b, c, d∈ℝ. We have to prove that θ…

Q: Let : [0, 1] → [0.c], te- and let w be a 1-form on R. What and foe, and why? is the relation between…

A:

Q: 6. Define the function E : Z → Z by E(n) 2n. Prove that E(n) is one-to-one, but not onto.

A: We will use the definition of one to one functions and onto functions to prove this.

Q: 6. Let f: A B be bijective. Prove that f-¹ of = A. -

A: