CS151 2005-2006 Tests 1&2 Repeat
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Q1 Prove the following statement true or false using truth tables: [4 marks]

  not(if A then B) = not(A) or B

Q2 Prove the following statement true or false using truth tables: [4 marks]

  if A then B = A and (if not(B) then false)

Q3 Prove that A is a subset of B where A = {x : x = 2c+1, c \in \naturalset} and B = \integerset. [5 marks]

Q4 Prove that B is not a subset of A. [2 marks]



CS151 2005-2006 Test 3 Repeat
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Q1 Write out the elements of the power set of {a, b, \emptyset, {a, b}}. [3 marks]

Q2 Write out the elements of {a, {a, b}} x {\emptyset}. [3 marks]

Q3 Let R = {(a, 5), (b, 6), (b, 5)} \subset {a, b, c} x {5, 6, 7}. State the minimum changes required to convert R into a
(total) function. [3 marks]

Q4 State the minimum number of changes required to convert R into a bijection. [2 marks]