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4 marksLogic and Boolean Algebra

CAPE Applied Mathematics Unit 2 · 2016 · Paper 2 · Question 1(a)(ii)

Boolean equivalence proof.

Show that (p ∧ ~q) ∨ (~p ∧ q) is equivalent to (p ∨ q) ∧ (~p ∨ ~q) using the laws of Boolean algebra.

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Other parts of this question

  1. 1(a)(i)State whether the 40 buses owned by "I'll take you there tours" constitute a sample or a population.[1 mark]
  2. 1(a)(ii)State whether 40 of the persons who attended the health seminar last week constitute a sample or a population.[1 mark]
  3. 1(b)(i)a)State ONE reason why visiting beauty shops on Saturday morning to interview a selection of customers buying the product may be unsatisfactory.[1 mark]
  4. 1(b)(i)b)State ONE reason why posting a questionnaire on the manufacturer's Facebook page for fans or followers to respond may be unsatisfactory.[1 mark]
  5. 1(b)(ii)a)Describe the sampling method used when all names are put into a box at the end of the exhibition and a random sample of 50 names is drawn.[1 mark]
  6. 1(b)(ii)b)Describe the sampling method used when every fifth name is selected from the list of names collected over the three days.[1 mark]
  7. 1(c)Using stratified random sampling to select a sample of 15 students from the group, determine how many boys will be in the sample.[2 marks]
  8. 1(d)State the advantage of using a stem-and-leaf diagram rather than grouping data into a frequency distribution.[1 mark]
  9. 1(e)(i)Relative to the stem-and-leaf diagram, state what 4|6 represents.[1 mark]
  10. 1(e)(ii)Determine how many patients were in the sample.[1 mark]
  11. 1(e)(iii)Determine how many patients waited more than 35 minutes.[1 mark]
  12. 1(e)(iv)Determine the range of waiting times.[3 marks]
  13. 1(e)(v)Determine the median waiting time for the sample.[2 marks]
  14. 1(e)(vi)Calculate the interquartile range for the waiting time data.[3 marks]
  15. 1(a)(i)Show that (p ∧ ~q) ∨ (~p ∧ q) is equivalent to (p ∨ q) ∧ (~p ∨ ~q) using truth tables.[4 marks]
  16. 1(b)(i)Draw the switching circuit for (p ∧ ~q) ∨ (~p ∧ q).[3 marks]
  17. 1(b)(ii)Draw the switching circuit for (p ∨ q) ∧ (~p ∨ ~q).[3 marks]
  18. 1(c)Determine the Boolean expression for the output s in the given logic circuit.[3 marks]
  19. 1(d)(i)Write an expression in logical notation for: "If a person eats red meat then that person may have a high cholesterol reading or suffer a heart attack."[2 marks]
  20. 1(d)(ii)Write an expression in logical notation for: "If a person does not suffer a heart attack then that person has a normal cholesterol reading and does not eat red…[2 marks]
  21. 1(d)(iii)Construct a truth table for the statement in (d)(i) and state with a reason whether it is a tautology.[4 marks]

More practice: the rest of this paper · more Logic and Boolean Algebra questions · all CAPE Applied Mathematics Unit 2 past papers