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(Associativity ) Let f: A to B , g : B t...

(Associativity ) Let `f: A to B , g : B to C " and " h: C to `. Then prove that ( h o g) o f = h o ( g o f )`

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To prove the associativity of the composition of functions, we need to show that \((h \circ g) \circ f = h \circ (g \circ f)\). Here’s a step-by-step solution: ### Step 1: Understand the Functions Let \( f: A \to B \), \( g: B \to C \), and \( h: C \to D \) be functions. We need to prove that the composition of these functions is associative. ### Step 2: Choose an Element Let \( x \) be an arbitrary element in the set \( A \). ...
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