KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 1 of 8
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1 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 1 of 8 Q1. What is a Proposition? Q2. What are Simple and Compound Propositions? Q3. What is a Connective? Q4. What are Sentential Operators? Q5. What do you understand by Disjunction? Q6. What do you understand by Conjunction? Q7. What do you understand by a Conditional Statement? Q8. What do you understand by a Bi-Conditional Statement? Q9. What do the Following operators mean: v ^ ~ => <=> Q10. Define Implication. Q11. Give an algebraic equivalent of Implication. Q12. Define Equivalence. Q13. Give an algebraic equivalent for Equivalence. Q14. Complete the following Truth-table. P Q P v Q P ^ Q P => Q P <=> Q ~P Q15. Define Negation. Q16. Define Assertion. Q17. Expand WFF. Q18. What are Well-formed formulae? Q19. What do you understand by Truth Functional? Q20. Explain Antecedent. Q21. Explain Consequent.
2 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 2 of 8 Q22. Explain Contingency. Q23. Explain Tautology. Q24. Explain Fallacy. Q25. Explain Contradiction. Q26. What is a Consistent Statement? Q27. Explain the term Converse. Q28. Explain the term Inverse. Q29. Explain the term Contra-positive. Q30. What is Conditional Elimination? Q31. What is Bi-Conditional Elimination? Q32. What is a Truth Table? Q33. How many rows does a Truth-Table have? Q34. In what sequence should we fill the rows of a Truth-Table? Q35. State and show Transposition using a Truth Table. P Q Q36. Define Syllogism. Q37. What are Premises? Q38. What do you understand by Infer? Q39. Describe Modus Ponens. Q40. Algebraically prove Modus Ponens.
3 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 3 of 8 Q41. Draw a Truth-Table depicting Modus Ponens. P Q Q42. Give the Chain Rule. Q43. Draw a Truth-Table depicting the Chain Rule. Q44. Algebraically prove the Chain Rule. Q45. State True or False: p=>q = p +q Q46. State True or False: p<=>q = q<=>p Q47. State True or False: p<=>q = (p=>q).(q=>p) Q48. Show that x+x is a tautology and x.x is a fallacy using a Truth-Table. Q49. Express in propositional Logic- If you study, you pass Q50. Explain Logical formula does not have an ambiguity of English. Q51. Express using a Truth Table: A bulb glows if any 2 of 3 buttons are on. P Q R Q52. Express using a Truth Table: A whistle blows if 2 consecutive tracks out of 3 have a train on them. P Q R [END]
4 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 4 of 8 Q53. Complete the following table Gate Algebraic Gate Symbol Gate Algebraic Gate Symbol Symbol Symbol NOT NAND AND OR NOR XNOR XOR Q54. Complete the following table X Y Z XYZ X+Y+Z X Y Z XYZ X + Y + Z X Y Z Q55. Complete the following table Law Equation 1 Equation 2 (Equation 3) (Equation 4) Identity Idempotent Complementarity Involution Associative Commutative Distributive Absorption DeMorgans Theorm Q56. Which law is called the double inversion rule? Q57. State the principle of duality. Give the dual of A+0.B Q58. Give the precedence of basic gates. Q59. Express XOR using basic gates. Q60. Express XNOR using basic gates. Q61. State the principle of duality. Give the dual of A+0.B Q62. Prove both the laws of absorption algebraically Q63. Give the precedence of the Boolean operators. Q64. What is the precedence of XOR Q65. State True of False (i) A+(B.C)=A+B.+C (ii) A. B = A. B
5 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 5 of 8 Q66. Prove both the De Morgan s Theorems. Theorem I Theorem I Theorem II Theorem II Q67. Draw a circuit diagram using the least number of gates (without simplifying) for A + B C A Q68. Give the complement of A + B C + A (Note: do not simplify) Q69. Define with an example Sum Term: Product Term: Min term: Max term: SOP expression: POS expression: Canonical SOP Expression: Canonical POS Expression: Binary Codes: Grey Codes: m: M: Q70. Convert A+AB to canonical SOP for using the 3 methods 1. Truth Table Method 2. Algebraic Method 3. Shortcut Method A B Answer: Q71. Convert XY+Z to canonical SOP for using the 3 methods 1. Truth Table Method 2. Algebraic Method 3. Shortcut Method X Y Z Answer: Q72. Express f(a,b,c)=a b c+a bc+ab c +abc in shorthand notation using (i) (ii) m Q73. Express f(a,b,c)=(a +b +c).(a +b+c).(a+b +c ).(a+b+c ) in shorthand notation using (i) Π (ii) M
6 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 6 of 8 Q74. What is a Karnaugh Map? Q75. Write the decimal values of cells and a, b, c or d in the following Karnaugh Maps Q76. State True or False (a) We should first look for octets, then quads and then pairs. (b) We should try to overlap/roll cells to obtain the largest possible groups. (c) We should make minimum possible number of largest possible sized groups. (d) If there are 2 possibilities of forming a group, it doesn t matter which one we choose. Q77. Give 2 possible answers of f(a,b,c) = (2, 3, 4, 5, 6). Compare them using a truth table B C B C BC BC A B C A B C AB A B AC CB A 0 1 A B C B C BC BC 1 0 A A Q78. Define: Overlapping Q79. Define: Map Rolling Q80. Define: Redundant Group Q81. What is the pair reduction rule? Q82. What is the quad reduction rule? Q83. What is the octet reduction rule? Q84. Reduce the following maps assume f(a, b, c, d)
7 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 7 of 8 Q85. When is output 1 produced with a (i) XOR gate (ii) XNOR gate Q86. What is the other name foe the XOR gate? Q87. Write equations to derive the basic gates from universal gates Universal gates Q88. What is the design rule for NAND to NAND logic network? Q89. What is the design rule for NOR to NOR logic network? Q90. What are two level circuits? Q91. Where are the following used/applied Adders Decoders Encoders Multiplexers Q92. Identify the following circuits Draw a Full adder (Labelled) Draw an Octal to Binary Encoder (Labelled) Draw a 2x4 Decoder Q93. What is also called a data selector? Draw a 4x1 MUX
8 KP/Worksheets: Propositional Logic, Boolean Algebra and Computer Hardware Page 8 of 8 Q94. Prove using a truth table that ( A B C)' = A B C A B C Q95. Derive Difference and borrow expressions for a Half Subtractor. A B Q96. State applications and an example for the following a) Adder b) Encoder c) Decoder d) Multiplexer Q97. Design the NOR gate using the NAND Gate Q98. Express in SOP and POS: A Club s membership is granted if the candidate has any one of the following certificates: Sports & a local domicile, Community service & a local domicile, NCC & a local domicile. S C N D F( ) F(Π) Reduction Q99. (open) Q100. (open) END
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