Southern New Hampshire University
1) State whether each of the following is a statement or is not a statement and explain why. If it is a statement, give its truth value. a) Drink more water. This is a not a statement because it is a command. b) Paris is the capital city of the United States of America. This is a statement, although it is a false statement, it is still considered a statement whether it is true or false. c) Is it going to rain tomorrow? This is not a statement because it is a question.
2) Consider the two propositions. p: We can buy a book. q: We can go to a restaurant. Write each of the following statements in symbolic notation and as English sentences.
b) The disjunction (v) of p and q. We can buy a book, or we can go to a restaurant.
cannot go to a restaurant.
d) The negation (~) of the disjunction (v) of p and q. We cannot buy a book, or we cannot go to a restaurant.
3) Write the statement "Every number is more than its reciprocal" symbolically by first defining a predicate and then using a quantifier. "Every" is the quantifier, and "is more" is the predicate.
4) Let P(n): n2 =n +6. a) What is P(2) as a statement? 2=2+6 b) What is P(3) as a statement? 32=3+6 c) What is the truth value of Vn P(n)? This is a false statement because P(2) doesn't work as part of the statement. d) What is the truth value of n P(n)? This is a true statement because there are some values for x that fit the statement, such as P(3).
5) Complete a truth table for (p A ~q) v (~p A q). There are multiple ways to set up the
P T T F T
Q T F T F
(p A~q)
v(~p A q) F F T F
T F F
6) Use the following: p: I will watch TV. q: I have finished my homework. Write each of the following statements in terms of p, q, and logical connectives. a) I will watch TV if I have finished my homework. P = q
SNHU MAT230
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Module Two Homework
Southern New Hampshire University
b) I will watch TV only if I have not finished my homework. P - ~q c) I will watch TV is a necessary condition for I have finished my homework. P - q d) I will not watch TV is a sufficient condition for I have finished my homework. ~p = q e) I will watch TV if and only if I have finished my homework. P q
7) Consider the following statement: If it is Friday, then Emily will go to the museum. a) Write the contrapositive of that statement. If Emily does not go to the museum, then it is not Friday. b) Write the converse of that statement. If Emily goes to the museum, the