The Logic of Compound Statements - Chapter 1 and Bitwise handout

• Statements and connectives.
• Relationship between english statements and statement forms.
• Truth tables, tautologies, contradictions, logically equivalent forms, De Morgan's laws.
• Logical implication, contrapositive, converse, inverse, if and only if.
• Arguments, valid conclusions.
• Digital Logic Circuits.
• Bitwise Arithmetic (Bitwise handout)

Section	Practice Exercises
1.1	3, 5, 6, 10ac, 11, 12, 16, 18, 19, 25, 27, 29, 31, 37, 39, 41, 42, 45, 47, 50.
1.2	1, 3, 5, 9, 12, 16, 19, 20df, 21a, 22df, 23df, 29, 32, 35, 40, 43, 45, 47, 49.
1.3	1, 3, 6, 8, 13a, 22, 24, 25, 26, 27, 36, 37, 38a, 39, 41, 43.
1.4	3, 7, 11, 18, 20, 22, 24, 28, 30.
1.5	1, 4, 7, 10, 27, 29, 38, 41, 44, 47a

Introduction to Set Theory - Chapter 5

• Naive set theory and Venn diagram
• Universe, null set, number sets
• Set inclusion, set operations
• Cartesian products, power sets
• Disjointedness and partitions
• Proving and Disproving set identities
• Boolean Algebras

We cover the following sections of Chapter 5 at this point:

5.1	All.
5.2	Statement of Theorems 5.2.1 & 5.2.2 only. (See below for more 5.2 material)
5.3	All.

Section	Practice Exercises
5.1	1, 2, 4acd, 5, 7a, 8abfi, 9e, 10, 12, 18a, 19a, 20a, 21, 22ad, 23, 26, 27a, 28, 29a, 30.
5.2	1, 21.
5.3	1, 2, 3, 5, 6, 11, 13, 14, 15, 23, 24, 25, 26, 29, 32, 37ab, 39. 40, 44, 48, 51, 53.

The Logic of Quantified Statements - Chapter 2

• Quantifiers and manipulation of English statements and their equivalent symbolic form.
• Generalised De Morgan laws, multiple quantifiers.
• Counter-examples, necessary and sufficient conditions.
• Tilomino

Section	Practice Exercises
2.1	3, 4b, 5ac, 7ac, 9, 11, 13, 14, 16ace, 19, 26bd.2
2.2	1, 3, 11, 13, 20, 22, 27, 31, 33, 47.
2.3	2ab, 3ab, 11a, 12acd, 14, 15, 16, 19, 20a, 32, 33, 36, 38, 43a
2.4	1acd, 2, 3, 5, 7, 8, 9, 10, 16, 19ab, 21, 23, 25, 31, 33.

Proof Techniques - Chapter 3

• Axioms, theorems, lemmas and corollaries
• Proof structure
• Direct proofs: existential, by exhaustion, deduction, construction, counterexample
• Indirect proofs by contradiction, contraposition
• Common pitfalls and mistakes in proofs
• Algebraic axioms and divisibility in Z
• Prime and composite numbers
• Div, mod, quotient-remainder theorem
• Rational and irrational numbers
• Floor and Ceiling

Section	Practice Exercises
3.1	1, 2, 7, 9, 14, 17, 19, 22, 24, 25, 31, 34, 35, 36, 39, 40, 41, 43, 50.
3.2	4, 9, 12, 13, 14, 16, 18, 19, 20, 21, 31
3.3	1, 4, 6, 7, 8, 10, 12, 14, 15, 17, 19, 21, 22, 23, 24, 29, 33a
3.4	1, 3, 5, 20, 21, 23b, 24, 34, 35.
3.5	1, 3, 8, 12, 14, 17, 23, 26.
3.6	3, 5, 12, 16, 19, 23, 24, 25.
3.7	21.

Relations - Chapter 10

• Binary relations and directed graphs.
• Reflexivity, symmetry, transitivity, equivalence relations.
• Equivalence relations, equivalence classes, and partitions of a set.
• Antisymmetry, partial and total orders, Hasse diagrams.

Section	Practice Exercises
10.1	1, 5ab, 7a, 8, 12, 13, 19, 23, 25, 26, 28a, 29.
10.2	1, 3, 6, 9, 14, 15, 18, 21, 23, 26, 30, 31, 34, 43, 44, 45, 47, 50.
10.3	1, 2a, 3, 5, 7, 8, 10, 14a, 16a, 17a, 18, 23, 25, 27, 30, 31, 33, 36, 39ace, 40.
10.5	1ab, 2, 5, 8, 10, 11ab, 13, 15, 16a, 17a, 18, 21, 22, 24, 26, 31, 32, 33

Functions - Chapter 7

• Definitions and notation.
• One-to one and onto
• Inverse of a function
• Composition of functions
• Pigeonhole Principle
• Exponential and Logarithmic Functions

Section	Practice Exercises
7.1	1, 3ab, 6a, 7, 9, 13, 14, 23a, 27ac, 31.
7.2	1, 3, 5, 6, 7, 9, 12, 13, 14, 15, 16, 17, 21, 22, 24, 25, 26, 32, 36, 38, 39, 40.
7.3	1, 3, 5, 7, 9, 10, 12, 14, 17, 20, 22, 24, 25, 26, 29
7.4	1, 3, 7, 9, 13, 16, 18, 19, 21, 23, 26.
9.4	5, 9, 10, 13, 14, 15, 18, 20.