Consider the following binary operations on R: :RXR R ((a,b),(c,d)) (a + c,b+d) :RXR...

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Consider the following binary operations on R²: Ⓒ:R²XR² → R² ((a,b),(c,d)) →→→ (a + c,b+d) :R²XR² R² ((a,b),(c,d)) (ac- bd,bc+ad) (a) Show that is commutative. is associative. (b) Show that (c) Show that is distributive over Ⓒ. (d) Show that there is a neutral element for >. Consider the following binary operations on R²: Ⓒ:R²XR² → R² ((a,b),(c,d)) →→→ (a + c,b+d) :R²XR² R² ((a,b),(c,d)) (ac- bd,bc+ad) (a) Show that is commutative. is associative. (b) Show that (c) Show that is distributive over Ⓒ. (d) Show that there is a neutral element for >.

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Solution Consider the following binary operations on R2 R2 x R2 R2 abcd acbd R2 x R2 R2 abcd ac bdbc ad a Show that is commutative and associative b S... View the full answer