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Formal Logic
S e c t I o n 1 . 1 Review
tecHnIQueS
• Construct truth tables for compound wffs.
• Recognize tautologies and contradictions.
MAIn IdeAS
• Wffs are symbolic representations of statements.
• Truth values for compound wffs depend on the
truth values of their components and the types of
connectives used.
• Tautologies are “intrinsically true” wffs—true for
all truth values.
W
W
eXeRcISeS 1.1
1. Which of the following sentences are statements?
a. The moon is made of green cheese.
b. He is certainly a tall man.
c. Two is a prime number.
d. The game will be over by 4:00.
e. Next year interest rates will rise.
f. Next year interest rates will fall.
g. x
2
− 4 = 0
2. What is the truth value of each of the following statements?
a. 8 is even or 6 is odd.
b. 8 is even and 6 is odd.
c. 8 is odd or 6 is odd.
d. 8 is odd and 6 is odd.
e. If 8 is odd, then 6 is odd.
f. If 8 is even, then 6 is odd.
g. If 8 is odd, then 6 is even.
h. If 8 is odd and 6 is even, then 8 < 6.
3. Given the truth values A true, B false, and C true, what is the truth value of each of the following wffs?
a. A ` (B ~ C )
c. (A ` B)′ ~ C
b. (A ` B) ~ C
d. A′ ~ (B′ ` C )′
4. Given the truth values A false, B true, and C true, what is the truth value of each of the following wffs?
a. A S (B ~ C )
c. C S (A′ ` B′)
b. (A ~ B) S C
d. A ~ (B′ S C )
5. Rewrite each of the following statements in the form “If A, then B.”
a. Healthy plant growth follows from sufficient water.
b. Increased availability of information is a necessary condition for further technological advances.
c. Errors were introduced only if there was a modification of the program.
d. Fuel savings implies good insulation or storm windows throughout.
Formal Logic
S e c t I o n 1 . 1 Review
tecHnIQueS
• Construct truth tables for compound wffs.
• Recognize tautologies and contradictions.
MAIn IdeAS
• Wffs are symbolic representations of statements.
• Truth values for compound wffs depend on the
truth values of their components and the types of
connectives used.
• Tautologies are “intrinsically true” wffs—true for
all truth values.
W
W
eXeRcISeS 1.1
1. Which of the following sentences are statements?
a. The moon is made of green cheese.
b. He is certainly a tall man.
c. Two is a prime number.
d. The game will be over by 4:00.
e. Next year interest rates will rise.
f. Next year interest rates will fall.
g. x
2
− 4 = 0
2. What is the truth value of each of the following statements?
a. 8 is even or 6 is odd.
b. 8 is even and 6 is odd.
c. 8 is odd or 6 is odd.
d. 8 is odd and 6 is odd.
e. If 8 is odd, then 6 is odd.
f. If 8 is even, then 6 is odd.
g. If 8 is odd, then 6 is even.
h. If 8 is odd and 6 is even, then 8 < 6.
3. Given the truth values A true, B false, and C true, what is the truth value of each of the following wffs?
a. A ` (B ~ C )
c. (A ` B)′ ~ C
b. (A ` B) ~ C
d. A′ ~ (B′ ` C )′
4. Given the truth values A false, B true, and C true, what is the truth value of each of the following wffs?
a. A S (B ~ C )
c. C S (A′ ` B′)
b. (A ~ B) S C
d. A ~ (B′ S C )
5. Rewrite each of the following statements in the form “If A, then B.”
a. Healthy plant growth follows from sufficient water.
b. Increased availability of information is a necessary condition for further technological advances.
c. Errors were introduced only if there was a modification of the program.
d. Fuel savings implies good insulation or storm windows throughout.