Conditional Statements
ANSWERS
1. Rewrite statements to if-then form.
- If I catch the 9:00 ferry, then I will not be late.
- If I don't wash this dress, then I won't have anything to wear tonight.
- If you don't freeze, then I will shoot.
2. Construct truth tables
- p
~q 
~p
| p |
q |
~p |
~q |
p~q |
p ~q
~p |
| T |
T |
F |
F |
T |
F |
| T |
F |
F |
T |
T |
F |
| F |
T |
T |
F |
F |
T |
| F |
F |
T |
T |
T |
T |
- (p r)
(q
r)
| p |
q |
r |
pr |
q r |
(p r)
(q r) |
| T |
T |
T |
T |
T |
T |
| T |
T |
F |
F |
F |
F |
| T |
F |
T |
T |
T |
T |
| T |
F |
F |
F |
T |
F |
| F |
T |
T |
T |
T |
T |
| F |
T |
F |
T |
F |
F |
| F |
F |
T |
T |
T |
T |
| F |
F |
F |
T |
T |
T |
3. Write the negation, contrapositive, converse
and inverse of the following statements:
- If John can run to another town, then he can run more than five miles.
- If today is Christmas, tomorrow is Thursday.
Negation:
- John can run to another town and he cannot run more
than five miles.
- Today is Christmas and tomorrow is not Thursday.
Contrapositive:
- If John cannot run more than five miles, then he
cannot run to another town.
- If tomorrow is not Thursday, then today is not Christmas.
Converse:
- If John can run more than five miles, then he can
run to another town.
- If tomorrow is Thursday, then today is Christmas.
Inverse:
- If John cannot run to another town, then he cannot
run more than five miles.
- If today is not Christmas, then tomorrow is not
Thursday.
4. Convert only-if statements to if-then statements.
- He will graduate only if he finishes the major project.
Version 1: If he finishes the major project, then he will graduate.
(is not a correct translation)
Version 2: If he doesn't finish the major project, he won't graduate.
- She will go shopping with her friends only if she finishes her homework.
Version 1: If she finishes her homework, then she will go shopping.
(is not a correct translation)
Version 2: If she doesn't finish her homework, she won't go shopping.
