NAME______________________________________DATE______________________
GEOMETRY
Logic Worksheet #5: CONDITIONALS II
Write all answers for 1 – 15 on loose leaf and attach to this sheet.
In 1 – 4, write the converse, inverse, and contrapositive of the statement in symbolic
form.
1) p → q
2) t → ~ w
3) ~ m → p
4) ~ p → ~ q
In 5 – 6, write the converse of the statement in words.
5) If you buy Goal toothpaste, then your children will brush longer.
6) When you serve imported sparkling water, it shows that you have good taste.
In 7 – 8, write the inverse of the statement in words.
7) If you live to an old age, then you eat Nano yogurt.
8) If you drive a Superb car, then you’ll get good mileage.
In 9 – 10, write the contrapositive of the statement in words.
9) If you brush with Brite, then your teeth will be pearly white.
10) If you want a good job, then you’ll get a high school diploma.
In 11 – 15, a conditional statement is given. Write in words a) the converse, b) the
inverse, and c) the contrapositive of that conditional.
11) If today is Friday, then tomorrow is Saturday.
12) If Douglas does well in college, then he will apply to medical school.
13) Arlette will get a role in the play if she auditions.
14) If a man is honest, he does not steal.
15) If Julia doesn’t water the plants, then the plants will die.
In 16 – 24, circle the correct answer.
16) When p → q is true, which related conditional must be true?
(1)) q → p
(2) ~ p → ~ q
(3) p → ~ q
(4) ~ q → ~ p
17) Which is the contrapositive of “If winter comes, then spring is not far behind”?
(1) If spring is not far behind, then winter comes.
(2) If spring is far behind, then winter comes.
(3) If spring is not far behind, then winter does not come.
(4) If spring is far behind, then winter does not come.
18) Which is the converse of “If a polygon is a rectangle, then its area does not
equal l • w • h.
(1) If a polygon is not a rectangle, then its area does not equal l • w • h.
(2) If a polygon has area that equals l • w • h, then it is a rectangle.
(3) If a polygon has an area that does not equal l • w • h, then it is not a rectangle.
(4) If the area of a rectangle is l • w • h, then it is a polygon.
19. Which statement has the same truth value as ~m  p?
(1) m  ~p
(2) p  ~m
(3) ~p  ~m
20. If p  q is true, then ~q  ~p is
(1) sometimes true
(3) truth value cannot be determined
21. The inverse of p  ~q is
(1) ~p  ~q
(2) ~p  q
(4) ~p  m
(2) always true
(4) never true
(3) ~q  p
(4) q  ~p
22. Identify the truth value of "If 32 = 9, the 33 = 27.
(1) true
(2) false
(3) no truth value
(4) cannot be determined
23. What is the truth value of the statement "If 13 + 1 > 14, then 17 + 1 > 18"?
(1) true
(2) false
(3) no truth value
(4) cannot be determined
24. Identify the truth value of "If x is divisible by 6, then it is divisible by 3" for every
integer x.
(1) true
(2) false
(3) no truth value
(4) cannot be determined