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Let A = {xϵZ:0≤x≤12 }. Show that R = {(a,b) : a, b ϵA,|a−b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]. OR Show that the function f:R→R defined by f(x)=xx2+1∀ x ϵ R is neither one-one nor onto. Also, if g:R→R is defined as g(x) = 2x-1, find fog(x). |
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Answer» Let A = {xϵZ:0≤x≤12 }. Show that R = {(a,b) : a, b ϵA,|a−b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]. OR Show that the function f:R→R defined by f(x)=xx2+1∀ x ϵ R is neither one-one nor onto. Also, if g:R→R is defined as g(x) = 2x-1, find fog(x). |
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