Worksheet 10. (Sec 3.6-3.7) Please indicate the most suitable answer on blank near the right margin. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the negation of the conditional statement. 1) If she can't take out the trash, I will. 1) A) She can take out the trash, and I can't. B) She can't take out the trash, and I won't. C) If she can take out the trash, I can't. D) She can't take out the trash, I can't. 2) If I get a high-paying job, then I can pay off all my bills. 2) A) I get a high-paying job and can pay off all my bills. B) I get a high-paying job and I cannot pay off all my bills. C) I don't get a high-paying job and can pay off all my bills. D) I don't get a high-paying job and cannot pay off all my bills. Use the De Morgan law that states: ~() is equivalent to ~ p to write an equivalent English statement for the statement. 3) It is not true that Boston and Russia are both states. 3) A) If Boston is a state, then Russia is not a state. B) Boston is not a state and Russia is not a state. C) It is true that Boston and Russia are both states. D) Boston is not a state or Russia is not a state. Use De Morgan's laws to write a negation of the statement. 4) She is not older than 21 and he is older than 21. 4) A) It is not true that she is older than 21 or he is not older than 21. B) She is older than 21 or he is not younger than 21. C) She is older than 21 or he is not older than 21. D) She is older than 21 but he is not older than 21. Use a truth table to determine whether the symbolic form of the argument is valid or invalid. 1
5) 5) p r ~ r q A) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) F T T F T F F T F B) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) T T F T F F T T F T F T F T F F T F T F F F F F T F F F T T F T F F T F F T F F T F T T F C) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) F T T F T F F T T F F F T T T T F T Symbolic argument is valid. 2
D) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) F T T F T F F T T 6) () (q r) 6) p r A) Valid B) Invalid SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Translate the argument into symbolic form. Then use a truth table to determine whether the argument is valid or invalid. (Ignore differences in past, present, and future tense.) 7) If it is July or August, then I am living at the beach 7) I am not living at the beach. It is neither July nor August. 3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the passage in the form of an argument using the following simple statements: p: The "diamond" is a fake. q: Peter will be unhappy for weeks. The argument's conclusion should be: The diamond must not have been a fake. Determine if the argument is valid or invalid. 8) Peter bought a "diamond" from a street vendor. I was sure it was a fake and that it would make 8) Peter miserable for weeks. But I saw him a few days later. He had got the "diamond" appraised and looked quite happy... A) p The argument is invalid. C) The argument is invalid. B) D) The argument is valid. The argument is valid. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw a valid conclusion from the given premises. 9) If I work in the garden, my back gets sore. 9) If my back gets sore, I take a hot bath Therefore... 4
Translate the argument into symbolic form, then use the table below to determine whether the argument is valid or invalid. Indicate valid/invalid and identify the type of answer. VALID ARGUMENTS Direct Contrapositive p q INVALID ARGUMENTS Disjunctive ~ p q p Transitive q r ~ r Fallacy of the Converse q p Fallacy of the Inverse ~ p Misuse of Disjunctive p q Misuse of Transitive q r r p ~ r 10) If Fred studies hard, then he gets a good grade. 10) Fred got a good grade. He studies hard. 11) If he wants to come, he will say so. 11) If he says so, then he will come. If he comes, that means he wants to. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use an Euler diagram to determine whether the argument is valid or invalid. 12) All insects have six legs. 12) No spiders are insects. Therefore, no spiders have six legs. 13) Some people enjoy walking. 13) Some people enjoy swimming. Therefore, some people who enjoy walking enjoy swimming. 14) All soda pops are carbonated. 14) All diet colas are soda pops. Therefore, all diet colas are carbonated. 5