CSE1203
Class Test 1, Fall 2013
Outline:
Chapter 1. Logic and Proofs
Topic 1.1. Propositional Logic
1. Propositions and Negation of a Proposition.
2. Compound Propositions involving common binary operators (connectives): Conjunction,
Disjunction, Exclusive Disjunction.
3. Conditional Statements; Truth tables for p  q, (p  q), p  q, Converse, Inverse and
Contrapositive of a Conditional Statement, and their truth tables.
4. Biconditional Statements; Truth tables for p  q, q  p, p  q, q  p.
5. Tautology, Contradiction, Contingency, Equivalence of two compound propositions and Order
of precedence of logical operators.
6. Common propositional equivalences and their verification using truth tables.
7. Proof of new propositional equivalences using common ones.
Topic 1.2. Predicate Logic
1. Predicates and Universe of discourse.
2. Quantification, Universal Quantifier, Existential quantifier, and Negation of quantified
predicates.
3. Expressing natural language sentences with quantified predicates and logical connectives.
Sample questions:
1. Show that the Contrapositive of a Conditional is logically equivalent to it. (2)
2. How do you define a predicate? Name the common quantifiers for predicates. (2)
3. Prove using truth tables that (q  p)  (p  q) is a Tautology. (2.5)
4. Prove using the laws of propositional logic that ((p  q)  q)  ((p  q)  p)  p  p. (3.5)
5. Show that the Converse and Inverse of a Conditional are logically equivalent to each other. (2)
6. How do you define a proposition? Explain the concept of conjunction of two propositions. (3)
7. What is a contradiction? Show that (p  q)  (p  q) is a contradiction. (3)
8. Illustrate the concepts of quantified predicates and their negations. (4)
9. Describe exclusive disjunction of propositions. (3)
10. Write down the Commutative, Associative, Distributive and DeMorgan’s laws of propositional
logic. (4)
11. Verify one of the Distributive laws of propositional logic using truth tables. (3)
12. Prove using the laws of propositional logic that (p  (q  p))  p and (q  (p  q))  (p 
q) are Contradictions. (3+3)
13. Prove using the laws of propositional logic that (q  (p  q))  q and ((p  q)  (q  p))
 p are Tautologies. (3+3)
14. Express the following two sentences with quantified predicates and logical connectives: (2+2)
Some of the students must solve all the problems.
A newcomer can’t participate in any of the events.