Section 1.12: The Biconditional
Exercises
Write out the truth tables for the following logical expressions. (You might want to do it
as just one or two really big tables.)
1. p q
2. p q
3. q p
4. q p
5. p q
6. p ^ q
7. pq
8. p q
9. pq
10. p q
11. p q
12.
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Section 1.4: Venn Diagrams
Exercises
Draw Venn diagrams using two sets A and B, shading in the appropriate regions for the
following situations.
1. AB
2. A B
3.
A B
4.
A B (this would just be the negation of #2)
5.
AB
6. A( A B)
7. A(AB)
Draw Venn
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Section 1.2: Subsets
Exercises
Let A= cfw_1, 3, 5, 7, 9, B= cfw_5, 6, 7, 8, C = cfw_3, 6, 9, 12, D = cfw_0, 1, 2, 3, 15. State
whether the following are true or false.
1. A B
2. D N
3. A Z
4. cfw_3, 6 C
5. B B
6. 7 C
7. 7 D
8.
Let A= cfw_2, 4, 6,
Section 1.10: More Laws of Logic
Exercises
(Note that these are the same exercises as at the beginning of section 1.5, but with a little
twist.) Let p be Rich is seven feet tall and q be Susan has brown hair. Translate the
following English sentences into
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Section 1.1: Sets
Exercises
Are the following sets equal?
1. cfw_1, 1, 1, 2, 2, 3 and cfw_1, 2, 2, 3, 3, 3
2. cfw_1, 2, 3 and cfw_3, 2, 1
3. cfw_4, 5, 6 and cfw_x | x is a natural number between 4 and 6
4. cfw_x | x is a natural number less than 5
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Section 1.3: Operations on Sets
Exercises
Let A = cfw_ x | x is an even natural number and B = cfw_1, 0, 1. Are the following
statements T (true) or F (false)?
1. A B =cfw_0
2.
B N cfw_1, 0, 1, .
3.
B Z
4.
A
5.
Z N=Z
6.
BA=B N
7.
0A
8.
A=A
9.
Z=A
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Section 1-5: Introduction to Logic
Exercises
State whether the following sentences are propositions.
1. On September 6, 2006, mathematicians proved that 232582657-1 was a prime number.
2. Will you marry me?
3. Python is her favourite computing lang
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Section 1.7: The Algebra of Sets
Exercises
Give the membership tables for the following expressions.
1. AA
2. AU
3. A
4. A B
5. A B
6. A B
7. A(AB)
8. A (BC)
9. A B C
10. A C B A B
11. A B(A B )
12. (A B C )(A B C)
Are the resulting sets equal to e
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Section 1.8: Boolean Algebra
Exercises
Draw the gate representation for the following logical expressions.
1. A + B
2. A B
3. A B
4. A B
5. A+B
6. AB C
7. A B C
8. AB C
9. A B C
Write the Boolean expression which corresponds to the following gates
Section 1-6: Logical Equivalence
Exercises
Give the truth tables for the following logical expressions.
1. p^ p
2. p
3. p^ q
4. p q
5. p q
6. p( p ^q)
7. (pq)^r
8. pq r
9. (p q) p q
10. (p q) (p q)
Are the two expressions logically equivalent?
11. p^q and
Section 1.11: The Conditional
Exercises
In the following exercises, let p denote The movie was popular and q denote The
movie will make a lot of money. Translate the following propositions into English
sentences.
1. p q
2. p q
3. q p
4. q p
5. p q
6. p ^
Section 1.9: Laws of Logic
Exercises
1. Which of the following statements is always true?
a)
b)
c)
d)
Darth Vader is both evil and not evil.
Darth Vader is both evil and evil.
Darth Vader is either evil or evil.
Darth Vader is either evil or not evil.
2.