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MA3354 Discrete Mathematics
UNIT1
MA3354 Discrete Mathematics
UNIT1
1. Show that R→S can be derived from the premises P→(Q→ S) , ⎤ R V P , and Q.
2. Obtain Disjunctive normal form, conjuctive normal form
3. "one student in this class knows how to write programs in JAVA and Everyone who knows how to write "Someone in this class can get a high-paying job" programs in JAVA can get a high paying job imply a conclusion."Someone in this class can get a high-paying job
UNIT-2
1. Recurrence relations
2.Mathematical inductions-strong induction and well ordering
3. Basics of counting
UNIT-3
1. Isomorphism between two graph
2. Euler and Hamilton paths
3. Proving that the number of vertices of odd degree in any graph G is even
UNIT-4
1. State and prove lagrange's theorem**
2. Homomorphism, Commutative Ring
3. Proving that a group homomorphism preserves the identity element
UNIT-5
1. Show that every chain is a distributive lattice
2. Boolean Algebra full topic
3. Properties of lattices
1. Show that R→S can be derived from the premises P→(Q→ S) , ⎤ R V P , and Q.
2. Obtain Disjunctive normal form, conjuctive normal form
3. "one student in this class knows how to write programs in JAVA and Everyone who knows how to write "Someone in this class can get a high-paying job" programs in JAVA can get a high paying job imply a conclusion."Someone in this class can get a high-paying job
UNIT-2
1. Recurrence relations
2.Mathematical inductions-strong induction and well ordering
3. Basics of counting
UNIT-3
1. Isomorphism between two graph
2. Euler and Hamilton paths
3. Proving that the number of vertices of odd degree in any graph G is even
UNIT-4
1. State and prove lagrange's theorem**
2. Homomorphism, Commutative Ring
3. Proving that a group homomorphism preserves the identity element
UNIT-5
1. Show that every chain is a distributive lattice
2. Boolean Algebra full topic
3. Properties of lattices
**Very important questions are bolded and may be asked based on this topic
**Very important questions are bolded and may be asked based on this topic
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*These questions are expected for the exams This may or may not be asked for exams All the best.... from admin Santhosh
Thanks for your love and support guys keep supporting and share let the Engineers know about Us and leave a comment below for better improvements If there is any doubt feel free to ask me I will clear if I can or-else I will say some solutions ..get me through WhatsApp for instant updates ~$tuff$£ctorSYllabuSUNIT I LOGIC AND PROOFS
Propositional logic – Propositional equivalences - Predicates and quantifiers – Nested quantifiers –
Rules of inference - Introduction to proofs – Proof methods and strategy.
UNIT II COMBINATORICS
Mathematical induction – Strong induction and well ordering – The basics of counting – The
pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear
recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.
UNIT III GRAPHS
Graphs and graph models – Graph terminology and special types of graphs – Matrix representation
of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.
UNIT IV ALGEBRAIC STRUCTURES
Algebraic systems – Semi groups and monoids - Groups – Subgroups – Homomorphism’s –
Normal subgroup and cosets – Lagrange’s theorem – Definitions and examples of Rings and Fields.
UNIT V LATTICES AND BOOLEAN ALGEBRA
Partial ordering – Posets – Lattices as posets – Properties of lattices - Lattices as algebraic systems
– Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra – Sub
Boolean Algebra – Boolean Homomorphism.
UNIT I LOGIC AND PROOFS
Propositional logic – Propositional equivalences - Predicates and quantifiers – Nested quantifiers –
Rules of inference - Introduction to proofs – Proof methods and strategy.
UNIT II COMBINATORICS
Mathematical induction – Strong induction and well ordering – The basics of counting – The
pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear
recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.
UNIT III GRAPHS
Graphs and graph models – Graph terminology and special types of graphs – Matrix representation
of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.
UNIT IV ALGEBRAIC STRUCTURES
Algebraic systems – Semi groups and monoids - Groups – Subgroups – Homomorphism’s –
Normal subgroup and cosets – Lagrange’s theorem – Definitions and examples of Rings and Fields.
UNIT V LATTICES AND BOOLEAN ALGEBRA
Partial ordering – Posets – Lattices as posets – Properties of lattices - Lattices as algebraic systems
– Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra – Sub
Boolean Algebra – Boolean Homomorphism.