LOGIC

1. Symbolic Logic Worksheet 3
Name: ____________________________________ Score: ____________
Section: __________________________________ Date: ____________
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 – 14, tell if the sentence is true, false, or open.
11) Every square contains 4 right angles and every triangle contains 1 right angle.
______
12) Tuesday follows Monday and 1 + 2 = 3. _________
13) Most math books contain problems and 2/3 of 12 is 8. _________
14) x = 28 – 17 and x = 11. _________
In 15 to 21, 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.”

2. 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.
15) b Λ g 18) b Λ ~ d 19) ~ s Λ d 20) ~ d Λ ~ b
21) ~ (d Λ b)
In 22 – 29, give the word, phrase, or symbol that can be placed in the blank to make
the resulting sentence true.
22) When p is true and q is true, then p Λ q is ___________.
23) When p is false, then p Λ q is __________.
24) If p is true, or q is true, but not both, then p Λ q is __________.
25) When p Λ q is true, then p is ______ and q is _________ .
26) When p Λ ~ q is true, then p is ______ and q is ________.
27) When ~ p Λ q is true, then p is ______ and q is ________.
28) When p is false and q is true, then ~ (p Λ q) is ________.
29) If both p and q are false, then ~ p Λ ~ q is ________.
30) When p and q represent two simple sentences, the conditional if p then q is written
symbolically as ________________.
31) The conditional if q then p is written symbolically as ______________.
32) The conditional p → q is false only when p is ________ and q is __________.
33) When the conclusion q is true, the p → q must be _____________.
34) When the hypothesis p is false, the p → q must be ______________.
35) If the hypothesis p is true and the conditional p → q is true, then the conclusion q
must be ___________.
In 36 – 39, 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.”
36) I will study or I will not pass the test. ______________
37) I will study and I will pass the test. ______________
38) I am not foolish and I will pass the test. ______________
39) I will study and I will pass the test, or I am foolish. ______________

3. In 40 – 49, 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
40) A meter contains 1,000 millimeters or a kilometer is 1,000 meters. _______________
41) A meter contains 100 centimeters or a meter is a liquid measure. ________________
42) A meter contains 100 centimeters or 1,000 millimeters. _________________
43) A kilometer is not 1,000 meters or a meter does not contain 100 centimeters.
_____________
44) A meter is a liquid measure or a kilometer is 1,000 meters. ______________
45) A meter is a liquid measure and a meter contains 100 centimeters. _____________
46) It is not the case that a meter contains 100 centimeters or 1,000 millimeters.
_____________
47) It is false that a kilometer is not 1,000 meters or a meter is a liquid measure.
_____________
48) A meter contains 100 centimeters and 1,000 millimeters or a meter is a liquid
measure. ___________________
49) It is not true that a meter contains 100 centimeters or a meter is a liquid
measure. _______________
In 50 – 56, give the word, phrase, or symbol that can be placed in the blank to make
the resulting sentence true.
50) When p is true, then p V q is ___________.
51) When q is true, then p V q is ___________.
52) When p is false and q is false, then p V q is _____________.
53) When p v ~ q is false, then p is _________ and q is __________.
54) When ~ p V q is false, then p is _________ and q is __________.
55) When p is false and q is true, then ~ (p V q) is _________.
56) When p is false and q is true, then ~ p V ~ q is _________.