PYQ Vault
EbooksTutor

Simplify a statement pattern to an equivalent one using the laws of logic

This type of question, asked 19 times: 4 May 2023 S1, 10 May 2023 S2, 16 May 2023 S1, 10 May 2024 S1, 11 May 2024 S1, 11 May 2024 S2, 14 May 2024 S2, 20 Apr 2025 S1, 21 Apr 2025 S1, 11 Apr 2026 S1, 18 Apr 2026 S1, 19 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S1, 14 May 2026 S2, 15 May 2026 S1, 15 May 2026 S2, 19 May 2026 S1, 19 May 2026 S2. All 19 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 May 2023 S1

    104
    The statement pattern [p∧(q∨r)]∨[∼r∧∼q∧p][p\wedge(q\vee r)]\vee[\sim r\wedge\sim q\wedge p] is equivalent to

    Tap an option to check your answer.

  2. Question 2

    10 May 2023 S2

    118
    The expression ((p∧q)∨(p∨∼q))∧(∼p∧∼q)((p\wedge q)\vee(p\vee\sim q))\wedge(\sim p\wedge\sim q) is equivalent to

    Tap an option to check your answer.

  3. Question 3

    16 May 2023 S1

    102
    The proposition (∼p)∨(p∧∼q)(\sim p) \vee (p \wedge \sim q) is equivalent to

    Tap an option to check your answer.

  4. Question 4

    10 May 2024 S1

    111
    The statement [∼(∼p∨q)∨(p∧r)]∧(∼q∧r)[\sim(\sim p\vee q)\vee(p\wedge r)]\wedge(\sim q\wedge r) is equivalent to

    Tap an option to check your answer.

  5. Question 5

    11 May 2024 S1

    144
    The statement pattern p→∼(p∧∼q)p \to \sim(p \wedge \sim q) is equivalent to

    Tap an option to check your answer.

  6. Question 6

    11 May 2024 S2

    140
    The logical statement (∼(∼p∨q)∨(p∧r))∧(∼q∧r)(\sim(\sim p\vee q)\vee(p\wedge r))\wedge(\sim q\wedge r) is equivalent to

    Tap an option to check your answer.

  7. Question 7

    14 May 2024 S2

    138
    The statement [p∧(q∨r)]∨[∼r∧∼q∧p][p\wedge(q\vee r)]\vee[\sim r\wedge\sim q\wedge p] is equivalent to

    Tap an option to check your answer.

  8. Question 8

    20 Apr 2025 S1

    118
    The logically equivalent statement of (∼p∧q)∨(∼p∧∼q)∨(p∧∼q)( \sim p \land q) \vee ( \sim p \land \sim q) \vee (p \land \sim q) is

    Tap an option to check your answer.

  9. Question 9

    21 Apr 2025 S1

    138
    The logical statement [∼(∼p∨q)∨(p∧r)]∧(∼q∧r)\left\lbrack \sim\left( \sim p\vee q \right)\vee\left( p\land r \right) \right\rbrack\land\left( \sim q\land r \right) is equivalent to

    Tap an option to check your answer.

  10. Question 10

    11 Apr 2026 S1

    61
    The statement pattern (p∨q)→∼r(p \vee q) \to \sim r is logically equivalent to

    Tap an option to check your answer.

  11. Question 11

    18 Apr 2026 S1

    60
    The correct logical equivalence from the following is /are ___ (I) p→(q→r)≡(p∧q)→rp \to (q \to r) \equiv (p \wedge q) \to r (II) (p→q)→r≡p→(q∨r)(p \to q) \to r \equiv p \to (q \vee r) (III) (p→q)→r≡(p→r)∧(∼q→r)(p \to q) \to r \equiv (p \to r) \wedge (\sim q \to r) (IV) p→(q→r)≡q→(p→r)p \to (q \to r) \equiv q \to (p \to r)

    Tap an option to check your answer.

  12. Question 12

    19 Apr 2026 S1

    63
    The logical statement (p∨q)∧[(∼p∧q)∨(p∧∼q)]∧∼q(p \vee q) \wedge [(\sim p \wedge q) \vee (p \wedge \sim q)] \wedge \sim q is logically equivalent to ...

    Tap an option to check your answer.

  13. Question 13

    13 May 2026 S2

    66
    The compound statement [∼(p→q)∨∼(p∧r)]∧p[\sim(p \to q) \vee \sim(p \wedge r)] \wedge p is logically equivalent to:

    Tap an option to check your answer.

  14. Question 14

    14 May 2026 S1

    63
    A statement logically equivalent to the statement pattern ∼[(p→∼q)∧(∼q∨p)]\sim[(p \to \sim q) \wedge (\sim q \vee p)] is

    Tap an option to check your answer.

  15. Question 15

    14 May 2026 S2

    64
    [(p∧q)∨(∼r∨∼s∨∼t)]∧[(p∧q)∨(r∧s∧t)]≡[(p \wedge q) \vee (\sim r \vee \sim s \vee \sim t)] \wedge [(p \wedge q) \vee (r \wedge s \wedge t)] \equiv

    Tap an option to check your answer.

  16. Question 16

    15 May 2026 S1

    64
    The logical expression [∼(p→q)∧(q→p)]∨∼(p↔q)[\sim(p \rightarrow q) \wedge (q \rightarrow p)] \vee \sim(p \leftrightarrow q) is equivalent to:

    Tap an option to check your answer.

  17. Question 17

    15 May 2026 S2

    66
    The statement (p∧(∼q))∨((∼p)∧q)∨((∼p)∧(∼q))(p \wedge (\sim q)) \vee ((\sim p) \wedge q) \vee ((\sim p) \wedge (\sim q)) is equivalent to :

    Tap an option to check your answer.

  18. Question 18

    19 May 2026 S1

    65
    The statement pattern p→(q→p)≡p \rightarrow (q \rightarrow p) \equiv

    Tap an option to check your answer.

  19. Question 19

    19 May 2026 S2

    59
    The statement pattern [p∧(q∨r)]∨[∼r∧∼q∧p][p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p] is equivalent to _____

    Tap an option to check your answer.