• ChrisS
Determine whether the given map $\phi$ is an isomorphism of the first binary structure with the second. If it is not an isomorphism, why not? $<\mathbb{Q},*>\ with\ <\mathbb{Q},*>\ where\ \phi(x)=x^{2}\ for\ x \in \mathbb{Q}$ I have the one-to-one requirement $If\ \phi(x)=\phi(y) then\ x^{2}=y^{2}$ $Then\ \sqrt{x^{2}}=\sqrt{y^{2}}$ So x=y Thus the map is one-to-one. Now I need to show that it is onto and I need to show $\phi(x*y)=\phi(x)*\phi(y)$
Mathematics
• Stacey Warren - Expert brainly.com
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SOLVED
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