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Logic and Boolean Algebra · CAPE Applied Mathematics Unit 2

46 past-paper questions on Logic and Boolean Algebra, part of Module 1: Discrete Mathematics, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

Practise Logic and Boolean Algebra
  1. 2(a)3 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Express in words: ~p ^ ~q.
  2. 2(b)3 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Determine the truth value of the statement: 'London is in England or 2 x 3 = 5'.
  3. 2(c)5 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2By constructing the truth table for the proposition (p ^ q) => (p v q), determine whether this proposition is a tautology or a contradiction.
  4. 2(d)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Represent the Boolean expression (A ^ ~B) v [(~A v C) ^ B] as a switching circuit.
  5. 2(d)(ii)5 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Represent ~a ^ (a v b) as a logic circuit using only AND, OR and NOT gates.
  6. 2(e)5 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Use the laws of Boolean algebra to show that the Boolean expression (A ^ B) v (A ^ ~B) v (~A ^ ~B) is equivalent to A v ~B.
  7. 2(a)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Design a switching circuit to allow current to pass when and only when at least TWO members vote 'yes'.
  8. 2(b)5 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Construct a truth table to show that the proposition (~p ∨ ~q) ⇒ (p ∧ ~q) always takes the value of p.
  9. 2(c)5 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2If a ⇒ b is equivalent to ~a ∨ b, draw a circuit for a ⇒ b using OR and NOT gates only.
  10. 1(a)5 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Construct a truth table to show that the proposition (~ p ˅ ~ q) ⇒ (p ˄ ~ q) ALWAYS takes the value of p.
  11. 1(b)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Write the Boolean expression for the given logic circuit.
  12. 1(c)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Draw a switching circuit to represent the expression (a ˄ b) ˅ [a ˄ (~ b ˅ c)].
  13. 1(d)(i)a)2 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Express the statement 'If there is a west wind then we shall have rain' in logic form using the connectives ~ and ⇒.
  14. 1(d)(i)b)2 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Express the statement 'If there is no rain then the west wind does not blow' in logic form using the connectives ~ and ⇒.
  15. 1(d)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Construct a truth table to prove that the statements in parts (d)(i)a) and (d)(i)b) are equivalent.
  16. 1(e)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Use de Morgan's laws to prove that ~ [(p ˄ q) ˅ ~ p] = ~ q ˄ p.
  17. 1(a)5 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Construct the truth table for (p \wedge q) \wedge \sim(p \vee q).
  18. 1(b)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2State, with reason, whether (p \wedge q) \wedge \sim(p \vee q) is a tautology or a contradiction.
  19. 1(c)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Write a statement to show the proposition that is logically equivalent to \sim(p \vee q).
  20. 1(d)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Using de Morgan's Law, or otherwise, write an equivalent statement to 'It is not true that it is hot and sunny.'
  21. 1(e)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Draw the circuit represented by this expression.
  22. 1(e)(ii)5 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Simplify this Boolean expression to obtain an equivalent expression and draw the corresponding circuit.
  23. 1(f)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Use logic gates to represent the expression \sim[(p \wedge q) \vee r].
  24. 1(a)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2State the contrapositive of p ⇒ ~q.
  25. 1(b)5 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Construct a truth table for the inverse of p ⇒ ~q.
  26. 1(c)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Construct a truth table for (p → q) ˅ (q → r).
  27. 1(c)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Hence, state with reason, whether (c)(i) is a tautology or a contradiction.
  28. 1(d)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Determine the Boolean expression for the given logic circuit.
  29. 1(e)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Draw a switching circuit for the Boolean expression A ˅ (B ˄ C).
  30. 1(e)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Use the distributive law to expand the Boolean expression A ˅ (B ˄ C).
  31. 2(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Represent the circuit as a Boolean expression.
  32. 2(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Construct its truth table.
  33. 2(b)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2By constructing a truth table, determine whether (p ∧ q) → p is a tautology or a contradiction.
  34. 2(c)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Write down a Boolean expression for the given circuit.
  35. 2(c)(ii)8 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Simplify the expression obtained in (c) (i) above and hence draw the corresponding circuit.
  36. 1(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Show that (p ∧ ~q) ∨ (~p ∧ q) is equivalent to (p ∨ q) ∧ (~p ∨ ~q) using truth tables.
  37. 1(a)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Show that (p ∧ ~q) ∨ (~p ∧ q) is equivalent to (p ∨ q) ∧ (~p ∨ ~q) using the laws of Boolean algebra.
  38. 1(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Draw the switching circuit for (p ∧ ~q) ∨ (~p ∧ q).
  39. 1(b)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Draw the switching circuit for (p ∨ q) ∧ (~p ∨ ~q).
  40. 1(c)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the Boolean expression for the output s in the given logic circuit.
  41. 1(d)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Write 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."
  42. 1(d)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Write 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 meat."
  43. 1(d)(iii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Construct a truth table for the statement in (d)(i) and state with a reason whether it is a tautology.
  44. 1(b)2 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Write the contrapositive of p \rightarrow \sim q.
  45. 1(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Use a truth table to show that for any propositions, p and q, p \Rightarrow q \Leftrightarrow \sim p \vee q.
  46. 1(b)(ii)5 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Using the laws of Boolean algebra, show that for any two propositions, p and q, \sim(p \vee \sim(p \wedge q)) is a contradiction.

Related topics in Module 1: Discrete Mathematics