Math 102
Exam 2: Additional Practice Problems
1. Negate each of the following statements, then rewrite them as English sentences:
(a) This summer I will get a job or I will take classes.
(b) If I eat my vegetables then I will get dessert
2. Given p: I studied for this exam, q: I got a good grade on this exam, r: I understand truth tables, and s: I am not
good at doing proofs, translate the following statements into words:
(a) p↔(∼s∨ ∼ r)
(b) (p→(r∧(∼s)) →q
3. (a) Explain, in your own words, the difference between “exclusive or” and “inclusive or”
(b) Give real world examples that illustrate both “exclusive or” and “inclusive or”
4. Given the statements: p: There is a full moon tonight, and q: I will go for a walk on the beach
(a) Write the conditional statement relating pto qin words.
(b) Write the converse in words.
(c) Write the inverse in words.
(d) Write the contrapositive in words.
(e) Indicate which of these statements above are logically equivalent to each other. You do not need to prove your
answer.
5. According to one of DeMorgan’s Laws, ∼(p∨q) is logically equivalent to (∼p)∧(∼q). Use truth tables to prove that
these two statements are logically equivalent. Then, explain in your own words why the fact that these two statements
are equivalent makes sense.
6. Given that pis true, qis false, ris true, and sis true:
(a) What is truth value of the statement: ∼(p∨q)→(r∧ ∼ s)
(b) How many rows would the full truth table for the expression ∼(p∨q)→(r∧ ∼ s) have?
7. Build truth tables for the following logical statements:
(a) (p∧(∼q)→q
(b) ∼q→(p∨ ∼ r)
(c) (p→q)↔∼ (q∧r)
8. Identify the form of the following arguments, and state whether the given argument is valid:
(a) If I have enough money saved up, then I will go to Mexico for Spring Break. I did not go to Mexico for Spring
Break. Therefore, I did not have enough money saved up.
(b) If I lie on my tax return, then I will get audited by the IRS. I got audited by the IRS. Therefore, I lied on my tax
return.
(c) I will go to Mexico for Spring Break or I will spend Spring Break with my family. I did not spend Spring Break
with my family. Therefore, I went to Mexico for Spring Break.
