# Logic Problems

Problems

Let p = I finish my work. Let q = I go shopping.

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Write the following command sentences for # 1-10 in words:

1. ~p
2. ~q
3. p ˄ q
4. p ˅ q
5. p → q
6. p ↔ q
7. ~p ˄ q
8. p ˄ ~q
9. ~p → ~q
10. ~ p → q

Let p = Bob is smart. Let q = Bob passes the test.

Write each of the following statements for # 11-20 in symbolic form.

11. Bob is not smart.
12. Bob does not pass the test.
13. Bob is smart and Bob passes the test.
14. Bob is smart or Bob passes the test.
15. If Bob is smart, then Bob passes the test.
16. Bob is smart if and only if Bob passes the test.
17. Bob is not smart, and Bob does not pass the test.
18. Bob is smart and Bob does not pass the test.
19. If Bob is not smart, then Bob passes the test.

20. If Bob passes the test, then Bob is smart

Problems # 21-24:

Identify the following compound statements as a negation, conjunction, disjunction, conditional, or biconditional.

21. Either Sally is sick, or Sally is lazy and unreliable.
22. If Bob goes to school and Bill goes to work, then Jane will have to be alone at home.
23. Sue is smart or Sue studies, and she is successful.
24. It is false that Jane is tall and Bob is short.

Problems # 25-35: Identify each statement according to the most dominant connective. Note: There is no actual statement needed for the ones that have an s in them and these don’t need to be transformed into words. So p, q, r, and s are just any given statements.

25. ~ p ˄ q → r
26. p ˄ q ↔ r
27. ~ p → ~ q
28. p ˄ q → r
29. p ˅ ( q → r )
30. p ↔ q ˄ r ˅ s
31. ~ ( p → q )
32. ( ~p ↔q ) v r
33. ~ p → r
34. ( p ˅ q ) ˄ ( r ˄ s )
35. p ˄ ( q ↔ r )

Problems # 36-41: State the most dominant connective. Write each symbolic statement in words. Use commas where appropriate.

36. p ˄ ( q ˅ r )
37. ( p ˅ q ) ˄ r
38. p ˅ q → r
39. p ˅ ( q → r )
40. ~ ( p ˄ r )
41. ~ p ˅ r

Problems # 42-47:

Add parentheses to form the type of compound statement indicated. If none are necessary, indicate the fact. Note: p, q, r, and s are just any given statements.

42. Conjunction s ˅ r ˄ p
43. Disjunction s ˅ r ˄ p
44. Negation ~ r ˄ p → s
45. Biconditional r ˄ s ↔ p ˄ q
46. Conditional r ↔s ˄ p → q
47. Disjunction r → s ˅ p. For more information on Logic Problems see this: https://www.dictionary.com/browse/logic

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