sol-midterm2 - MACM 101 — Discrete Mathematics I Outline...

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Unformatted text preview: MACM 101 — Discrete Mathematics I Outline Solutions to Exercises on Functions and Relations 1. Give a definition of a one-to-one function. Let f be a function from A to B . The function f is called one-to-one if and only if for any a,b ∈ A f ( a ) = f ( b ) implies a = b . 2. Give a definition of the composition of two functions. Let g be a function from A to B and f be a function from B to C . The composition of functions f and g , denoted by f ◦ g is the function from A to C defined by ( f ◦ g )( a ) = f ( g ( a )) . 3. Prove that for any sets A , B , and C [15] ( A − B ) − C = ( A − C ) − ( B − C ) . Draw Venn diagrams of both sides of the equality. Method 1. ( A − C ) − ( B − C ) = { a | a ∈ ( A − C ) ∧ a negationslash∈ ( B − C ) } = { a | a ∈ A ∧ a negationslash∈ C ∧ ¬ ( a ∈ ( B − C )) } = { a | a ∈ A ∧ a negationslash∈ C ∧ ¬ ( a ∈ B ∧ a negationslash∈ C } = { a | a ∈ A ∧ a negationslash∈ C ∧ ( a negationslash∈ B ∨ a ∈ C ) } = { a | a ∈ A ∧ (( a negationslash∈ C ∧ a negationslash∈...
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This note was uploaded on 10/09/2009 for the course MATH macm 101 taught by Professor Jcliu during the Spring '09 term at Simon Fraser.

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sol-midterm2 - MACM 101 — Discrete Mathematics I Outline...

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