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3. Let f: A→ Band g: B → Cdenote two functions. Show that if gofis 1-1, then fis 1-1. D JCI

3. Let f: A→ Band g: B → Cdenote two functions. Show that if gofis 1-1, then fis 1-1. D JCI

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Let \( f: A \to B \) and \( g: B \to C \) denote two functions. Show that if \( g \circ f \) is 1-1, then \( f \) is 1-1. 4. Let \( A, B, \) and \( C \) denote three sets. Show that \( A - (B \cap C) = (A - B) \cup (A - C) \). 5. Let \( n \) denote a positive integer, while \( x, y \) denote real numbers. Show that \(\left\lfloor \frac{n}{2} \right\rfloor \times \left\lceil \frac{n}{2} \right\rceil = \left\lfloor \frac{n^2}{4} \right\rfloor\).
Transcribed Image Text:3. Let \( f: A \to B \) and \( g: B \to C \) denote two functions. Show that if \( g \circ f \) is 1-1, then \( f \) is 1-1. 4. Let \( A, B, \) and \( C \) denote three sets. Show that \( A - (B \cap C) = (A - B) \cup (A - C) \). 5. Let \( n \) denote a positive integer, while \( x, y \) denote real numbers. Show that \(\left\lfloor \frac{n}{2} \right\rfloor \times \left\lceil \frac{n}{2} \right\rceil = \left\lfloor \frac{n^2}{4} \right\rfloor\).
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