Logic Worksheet #3:
In 1 – 10 write each sentence in symbolic form, using the given symbols.
Let p represent “It is cold.”
Let q represent “It is snowing.”
Let r represent “the sun is shining.”
1) It is cold and it is snowing.
2) It is cold and the sun is shining.
3) It is not cold.
4) It is not cold and the sun is shining.
5) It is snowing and the sun is not shining.
6) It is not cold and it is not snowing.
7) The sun is not shining and it is not cold.
8) The sun is not shining and it is cold.
9) It is not the case that it is cold and it is snowing.
10) It is not the case that it is snowing and it is not cold.
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In 11 – 17, tell if the sentence is true, false, or open.
11) France is in South America and Germany is in Asia. _________
12) Every square contains 4 right angles and every triangle contains 1 right angle. ______
13) Tuesday follows Monday and 1 + 2 = 3. _________
14) It is a math book and it contains problems. _________
15) Most math books contain problems and 2/3 of 12 is 8. _________
16) x = 28 – 17 and x = 11. _________
17) The Surgeon General of the U.S. has determined that cigarette smoking is dangerous
to your health and warning labels are printed on cigarette packs. ________
In 18 to 29, symbols are assigned to represent sentences.
Let b represent “A banjo is a stringed instrument.”
Let d represent “A drum is a stringed instrument.”
Let g represent “A guitar is a stringed instrument.”
Let s represent “She plays a guitar.”
For each sentence given in symbolic form: a) Write a complete sentence in words to
show what the symbols represent. b) Tell if the sentence is true, false, or open.
18) b Λ g
19) b Λ d
20) g Λ s
21) b Λ ~ d
22) b Λ ~ g
23) b Λ ~ s
24) g Λ ~ d
25) ~ s Λ d
26) ~ d Λ ~ b 27) ~ (d Λ b) 28) ~ (b Λ g) 29) ~ (g Λ s)
In 30 – 37, give the word, phrase, or symbol that can be placed in the blank to make the
resulting sentence true.
30) When p is true and q is true, then p Λ q is ___________.
31.) When p is false, then p Λ q is __________.
32) If p is true, or q is true, but not both, then p Λ q is __________.
33) When p Λ q is true, then p is ______ and q is _________ .
34) When p Λ ~ q is true, then p is ______ and q is ________.
35) When ~ p Λ q is true, then p is ______ and q is ________.
36) When p is false and q is true, then ~ (p Λ q) is ________.
37) If both p and q are false, then ~ p Λ ~ q is ________.
In 38 – 47, write each sentence in symbolic form, using the given symbols.
Let s represent “I will study.”
Let p represent “I will pass the test.”
Let f represent I am foolish.”
38) I will study or I am foolish.
39) I will study or I will not pass the test.
40) I will study and I will pass the test.
41) I will pass the test or I am foolish.
42) I am not foolish and I will pass the test.
43) I will not study or I am foolish.
44) I will study or I will not study.
45) I will study and I will pass the test, or I am foolish.
46) It is not true that I will study or I am foolish.
47) It is not the case that I will not study or I am not foolish.
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In 48 – 57, for each given statement: a) Write the statement in symbolic form, using the
symbols given below. b) Tell whether the statement is true or false.
Let c represent “A meter contains 100 centimeters.”
Let m represent “A meter contains 1,000 millimeters.”
Let k represent “A kilometer is 1,000 meters.”
Let l represent “A meter is a liquid measure.”
TRUE
TRUE
TRUE
FALSE
48) A meter contains 1,000 millimeters or a kilometer is 1,000 meters. _______________
49) A meter contains 100 centimeters or a meter is a liquid measure. ________________
50) A meter contains 100 centimeters or 1,000 millimeters. _________________
51) A kilometer is not 1,000 meters or a meter does not contain 100 centimeters.
_____________
52) A meter is a liquid measure or a kilometer is 1,000 meters. ______________
53) A meter is a liquid measure and a meter contains 100 centimeters. _____________
54) It is not the case that a meter contains 100 centimeters or 1,000 millimeters.
_____________
55) It is false that a kilometer is not 1,000 meters or a meter is a liquid measure.
_____________
56) A meter contains 100 centimeters and 1,000 millimeters or a meter is a liquid
measure. ___________________
57) It is not true that a meter contains 100 centimeters or a meter is a liquid measure.
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In 58 – 69, symbols are assigned to represent sentences.
Let b represent “Biology is a science.”
Let s represent “Spanish is a language.”
Let h represent “Homemaking is a language.”
Let d represent “it’s a difficult course.”
For each sentence given in symbolic form: a) Write a complete sentence in words to
show what the symbols represent. b) Tell if the sentence is true, false, or open.
58) s V h
59) b V s
60) d 61) ~ s V h
64) ~ b V ~ s 65) ~ (s V h) 66) s Λ h
62) ~ d
67) s Λ b
63) b V ~ h
68) ~ (~ b V s)
69) ~ (~ s V h)
In 70 – 76, give the word, phrase, or symbol that can be placed in the blank to make the
resulting sentence true.
70) When p is true, then p V q is ___________.
71) When q is true, then p V q is ___________.
72) When p is false and q is false, then p V q is _____________.
73) When p v ~ q is false, then p is _________ and q is __________.
74) When ~ p V q is false, then p is _________ and q is __________.
75) When p is false and q is true, then ~ (p V q) is _________.
76) When p is false and q is true, then ~ p V ~ q is _________.