Prove that if f:A→B and g:B→C and if g◦f is injective,then f must be injective.
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Originally Posted by hebby Prove that if f:A→B and g:B→C and if g◦f is injective,then f must be injective. $\displaystyle f(a)=f(a')\Longrightarrow gf(a)=gf(a')$ , but gf is injective so... Tonio
f must be injective ? thats it?
Originally Posted by hebby f must be injective ? thats it? errr....yes, of course, but you still need a little more work to do. Think. Tonio
well i wrote Suppose f(x) = f(y). Then g(f(x)) = g(f(y)), so, since g ◦ f is 1–1, it follows that x = y. Therefore, f is 1–1....is this ok?
Originally Posted by hebby well i wrote Suppose f(x) = f(y). Then g(f(x)) = g(f(y)), so, since g ◦ f is 1–1, it follows that x = y. Therefore, f is 1–1....is this ok? Very good. Tonio
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