MATH 1332 Section 1B

MATH 1332 Section 1B

Propositions and Truth Values

Multiple Choice

A Proposition? Determine whether the following statements are propositions, and give an explanation.

13. The sky is the limit.

• True

• False

Multiple Choice

A Proposition? Determine whether the following statements are propositions, and give an explanation.

15. Back to the future.

• True

• False

Fill in the Blank

Negation. Write the negation of the given proposition. Then state the truth value of the original proposition and its negation.

21. The Beatles were not a German band.

Multiple Choice

21. Original statement

P: The Beatles were not a German band.

• True

• False

Multiple Choice

21. Negation

Not P: The Beatles were a German band.

• True

• False

Multiple Choice

Multiple Negations. Explain the meaning of the given statement, which contains a multiple negation. Then answer the question that follows.

23. Sarah did not decline the offer to go to dinner. Did Sarah go to dinner?

• Sarah went to dinner.

• Sarah did not go to dinner.

Open Ended

And Statements. The following statements have the form p and q. State p and q, and give their truth values. Then determine whether the conjunction (the and statement) is true or false, and explain why.

31. Dogs are animals and oak trees are plants.

31. Dogs are animals and oak trees are plants.

p: Dogs are animals.

q: Oak trees are plants.

p is True

q is True

p and q is True

Open Ended

And Statements. The following statements have the form p and q. State p and q, and give their truth values. Then determine whether the conjunction (the and statement) is true or false, and explain why.

35. All birds can fly and some fish live in trees.

35. All birds can fly and some fish live in trees.

p: All birds can fly.

q: Fish live in trees.

p is True

q is False

p and q is False

Truth Tables. Make a truth table for the given statement. Assume that p, q, r, and s represent propositions.

37. q and r and s

Multiple Choice

Interpreting or. State whether or is used in the inclusive or ­exclusive sense in the following propositions.

39.I will either walk or ride a bike to the park.

• Inclusive

• Exclusive

Multiple Choice

Interpreting or. State whether or is used in the inclusive or ­exclusive sense in the following propositions.

43. I would like to scuba dive or surf on my next vacation.

• Inclusive

• Exclusive

Truth Tables. Make a truth table for the given statement. Assume that p, q, r, and s represent propositions.

45. r or s

Truth Tables. Make a truth table for the given statement. Assume that p, q, r, and s represent propositions.

49. p or q or r

Open Ended

Or Statements. The following statements have the form p or q. State p and q, and give their truth values. Then determine whether the disjunction (or statement) is true or false, and explain why.

51. Elephants are animals or elephants are plants.

51. Elephants are animals or elephants are plants.

p: Elephants are animals.

q: Elephants are plants.

p is true

q is false

p or q is true

Open Ended

Or Statements. The following statements have the form p or q. State p and q, and give their truth values. Then determine whether the disjunction (or statement) is true or false, and explain why.

53. 3×5=15 or 3+5=8

53. 3×5=15 or 3+5=8

p: 3x5=15

q: 3+5=8

p is true

q is true

Truth Tables. Make a truth table for the given statement. Assume that p, q, r, and s represent propositions.

57. if p, then r

Open Ended

If…then Statements. Identify the hypothesis and the conclusion in the following conditional propositions, and state their truth values. Then determine whether the entire proposition is true or false.

59. If trout can swim, then trout are fish.

59. If trout can swim, then trout are fish.

hypothesis: Trout can swim.

conclusion: Trout are fish.

The hypothesis is true.

The conclusion is true.

The conditional "If trout can swim, then trout are fish. " is also true.

Open Ended

If…then Statements. Identify the hypothesis and the conclusion in the following conditional propositions, and state their truth values. Then determine whether the entire proposition is true or false.

63. If trees can walk, then birds wear wigs.

63. If trees can walk, then birds wear wigs.

hypothesis: Trees can walk.

conclusion: Birds wear wigs.

The hypothesis is false.

The conclusion is false.

The conditional "If trees can walk, then birds wear wigs." is also true.

Open Ended

If…then Statements. Identify the hypothesis and the conclusion in the following conditional propositions, and state their truth values. Then determine whether the entire proposition is true or false.

65. If dogs can swim, then dogs are fish.

65. If dogs can swim, then dogs are fish.

hypothesis: Dogs can swim.

conclusion: Dogs are fish.

The hypothesis is true.

The conclusion is false.

The conditional "If dogs can swim, then dogs are fish." is false.