This document contains a symbolic logic worksheet with multiple choice, true/false, and fill-in-the-blank questions about representing sentences symbolically using logical connectives like conjunction, disjunction, negation, implication and equivalence. Students are asked to translate sentences between natural language and symbolic logic notation using assigned symbols.

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 _________.