Section 1.1 Statements, Symbolic Representation, and Tautologies
17
6. Rewrite each of the following statements in the form “If A, then B.”
a. Candidate Lu winning the election will be a sufficient condition for property taxes to increase.
b. The user clicks Pause only if the game level changes.
c. The components are scarce, therefore the price increases.
d. Healthy hair is a necessary condition for good shampoo.
7. Common English has many ways to describe logical connectives. Write a wff for each of the following
expressions.
a. Either A or B
b. Neither A nor B
8. Common English has many ways to describe logical connectives. Write a wff for each of the following
expressions.
a. B whenever A
c. A indicates B
b. A is derived from B
d. A exactly when B
9. Several forms of negation are given for each of the following statements. Which are correct?
a. The answer is either 2 or 3.
1. Neither 2 nor 3 is the answer.
2. The answer is not 2 or not 3.
3. The answer is not 2 and it is not 3.
b. Cucumbers are green and seedy.
1. Cucumbers are not green and not seedy.
2. Cucumbers are not green or not seedy.
3. Cucumbers are green and not seedy.
c. 2 < 7 and 3 is odd.
1. 2 > 7 and 3 is even.
3. 2 ≥ 7 or 3 is odd.
2. 2 ≥ 7 and 3 is even.
4. 2 ≥ 7 or 3 is even.
10. Several forms of negation are given for each of the following statements. Which are correct?
a. The carton is sealed or the milk is sour.
1. The milk is not sour or the carton is not sealed.
2. The carton is not sealed and also the milk is not sour.
3. If the carton is not sealed, then the milk will be sour.
b. Flowers will bloom only if it rains.
1. The flowers will bloom but it will not rain.
2. The flowers will not bloom and it will not rain.
3. The flowers will not bloom or else it will not rain.
c. If you build it, they will come.
1. If you build it, then they won’t come.
2. You don’t build it, but they do come.
3. You build it, but they don’t come.
11. Write the negation of each statement.
a. If the food is good, then the service is excellent.
b. Either the food is good or the service is excellent.
17
6. Rewrite each of the following statements in the form “If A, then B.”
a. Candidate Lu winning the election will be a sufficient condition for property taxes to increase.
b. The user clicks Pause only if the game level changes.
c. The components are scarce, therefore the price increases.
d. Healthy hair is a necessary condition for good shampoo.
7. Common English has many ways to describe logical connectives. Write a wff for each of the following
expressions.
a. Either A or B
b. Neither A nor B
8. Common English has many ways to describe logical connectives. Write a wff for each of the following
expressions.
a. B whenever A
c. A indicates B
b. A is derived from B
d. A exactly when B
9. Several forms of negation are given for each of the following statements. Which are correct?
a. The answer is either 2 or 3.
1. Neither 2 nor 3 is the answer.
2. The answer is not 2 or not 3.
3. The answer is not 2 and it is not 3.
b. Cucumbers are green and seedy.
1. Cucumbers are not green and not seedy.
2. Cucumbers are not green or not seedy.
3. Cucumbers are green and not seedy.
c. 2 < 7 and 3 is odd.
1. 2 > 7 and 3 is even.
3. 2 ≥ 7 or 3 is odd.
2. 2 ≥ 7 and 3 is even.
4. 2 ≥ 7 or 3 is even.
10. Several forms of negation are given for each of the following statements. Which are correct?
a. The carton is sealed or the milk is sour.
1. The milk is not sour or the carton is not sealed.
2. The carton is not sealed and also the milk is not sour.
3. If the carton is not sealed, then the milk will be sour.
b. Flowers will bloom only if it rains.
1. The flowers will bloom but it will not rain.
2. The flowers will not bloom and it will not rain.
3. The flowers will not bloom or else it will not rain.
c. If you build it, they will come.
1. If you build it, then they won’t come.
2. You don’t build it, but they do come.
3. You build it, but they don’t come.
11. Write the negation of each statement.
a. If the food is good, then the service is excellent.
b. Either the food is good or the service is excellent.