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Please handwriting
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answerhappygod
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Please handwriting
Please handwriting
QUESTION 3 (20 Marks) Use direct proof to proof that "if m+n and n+p are even integers, where m, n and p are integers, then m+ p is even". (a) (b) (c) Use proof by contradiction to prove the statement below: If s, t€ Z and s≥ 2, then st or S s/(t+1). Note: (1) (7 marks) 214 denotes 2 divides 4 and 2/3 denotes 2 does not divide 3. Definition of divisibility, ab if an only if ac = b where a, beZ and ce Zt. By De Morgan's Law, the negation of "st or s/(t+1)" is "st and s|(t+1)”. (6 marks) (iii) Use proof by contrapositive to prove the statement below: Let xe Z. If x² - 6x+5 is even, then x is odd. (7 marks)
QUESTION 3 (20 Marks) Use direct proof to proof that "if m+n and n+p are even integers, where m, n and p are integers, then m+ p is even". (a) (b) (c) Use proof by contradiction to prove the statement below: If s, t€ Z and s≥ 2, then st or S s/(t+1). Note: (1) (7 marks) 214 denotes 2 divides 4 and 2/3 denotes 2 does not divide 3. Definition of divisibility, ab if an only if ac = b where a, beZ and ce Zt. By De Morgan's Law, the negation of "st or s/(t+1)" is "st and s|(t+1)”. (6 marks) (iii) Use proof by contrapositive to prove the statement below: Let xe Z. If x² - 6x+5 is even, then x is odd. (7 marks)