QUESTION ONE (30 MARKS a) Determine the validity of the following argument S: Some crazy people...

  

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QUESTION ONE (30 MARKS a) Determine the validity of the following argument S₁: Some crazy people are dangerous S₂: All fanatics are crazy Conclusion: some fanatics are not dangerous. n(n+1) 2 b) Prove the proposition that the sum of n positive even integers is. c) Find all the integers such that 2 <8-3n≤18 d) Give an example of a non-trivial relation on the set A={1,2,3} which is i. Both symmetric and antisymmetric ii. Neither symmetric nor antisymmetric e) Solve the linear congruence equation 4x = 6(mod10) (3 marks) (4 marks) (3 marks) (2 marks) (2 marks) (4 marks) f) Find the product of the polynomials f(x) = 4x³ -2x² + 3x-1and g(x)=3x²-x-4 over Z5 (4 marks) (5 marks) g) Prove that (a+b)' = a¹*b' h) Given a binary on the set of integers given by a*b=a+b-ab. show that * is (3 marks) commutative and associative QUESTION ONE (30 MARKS a) Determine the validity of the following argument S₁: Some crazy people are dangerous S₂: All fanatics are crazy Conclusion: some fanatics are not dangerous. n(n+1) 2 b) Prove the proposition that the sum of n positive even integers is. c) Find all the integers such that 2 <8-3n≤18 d) Give an example of a non-trivial relation on the set A={1,2,3} which is i. Both symmetric and antisymmetric ii. Neither symmetric nor antisymmetric e) Solve the linear congruence equation 4x = 6(mod10) (3 marks) (4 marks) (3 marks) (2 marks) (2 marks) (4 marks) f) Find the product of the polynomials f(x) = 4x³ -2x² + 3x-1and g(x)=3x²-x-4 over Z5 (4 marks) (5 marks) g) Prove that (a+b)' = a¹*b' h) Given a binary on the set of integers given by a*b=a+b-ab. show that * is (3 marks) commutative and associative

Answer rating: 100% (QA)

Solution a The argument is invalid The premises do not necessarily lead to a conclusion Just because ... View the full answer