Logic Worksheet #3:
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. _____________________
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. ______________
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.” TRUE
Let m represent “A meter contains 1,000 millimeters.” TRUE
Let k represent “A kilometer is 1,000 meters.” TRUE
Let l represent “A meter is a liquid measure.” 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. _______________
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 62) ~ d 63) b V ~ h
64) ~ b V ~ s 65) ~ (s V h) 66) s Λ h 67) s Λ b 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 _________.
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