#### Topics

1. Define proposition.

A proposition is an elementary atomic sentence that may either be true or false but may take no other value. Propositions are also called sentences or statements.

2. What is compound proposition?

A compound proposition is one with two or more simple propositions as parts or what we will call components.

3. What is an operator or connective?

An operator or connective joins simple propositions into compounds, and joins compounds into larger compounds. We will use the symbols to designate the sentential connectives. They are called sentential connectives because they join sentences or propositions. The symbol is the only operator that is not a connective, it affects single statements only.

4. List different types of connectives or operators used in propositional logic.

i. Disjunctive (OR)

ii. Conjunctive (AND)

iii. Conditional (If…. Then/Implication)

iv. Bi-conditional (If and only If / Equivalence)

v) Negation (NOT)

5. What is Disjunctive connective?

Disjunctive (OR), represented by symbols + or V. Disjunction means one of the two arguments is true or both.

Eg: p+q (or pVq) means p OR q. it’s meaning is either p is true or q is true or both.

6. What is conjunctive connective?

Conjunctive (AND) connective represented by symbols . Conjunction means both arguments are true.

Eg. p.q or (p & q) means p AND q. it’s meaning is both p and q are true.

7. What is Conditional connective?

Conditional connective is also called IF…. Then or Implication. Represented by symbols . Implication means if one argument is true then other argument is true.

Eg: means If P then q. Its meaning is if p is true, then q is true.

8. What is B-conditional connective?

B-conditional connective is also called if and only of or Equivalence. Represented by symbols . Equivalence or biconditional means either both arguments are true or both are false.

Eg: means if and only if p is true then q is true. Its meaning is p and q are either both true or both false.

9. What is Negation operator?

Negation also called NOT. Not a connective actually just an operator. Represented by or ‘ or (bar). It is an operator that affects a single statement only and does not join two or more statements.

Eg: means NOT p. Its meaning is p is false.

10. Match the following.

 p+q equivalence p.q disjunction implication conjunction

 p+q disjunction p.q conjunction implication equivalence

11. Define truth value.

The truth value of a statement is its truth or falsity. All meaningful statements have truth values, whether they are simple or compound, asserted or negated.

12. Define truth table.

A truth table is a table which represents complete list of possible truth values of a proposition.

13. Draw the truth table of unary connective.

Truth table for Negation (NOT)

 P ˜P 0 1 1 0

14. Why negation is called as unary connective?

The negation operator, NOT operator works on single proposition, so it is called as unary connective.

If p denotes a proposition, then its negation will be denoted by If p is false then ˜p is true and if p is true then ˜p is false.

15. Draw the truth table for Disjunction (OR).

 p q p+q 00 1 1 0 1 0 1 0 1 1 1

16. Draw the truth table for Conjunction (AND)

 p q p+q 00 1 1 0 1 0 1 0 0 0 1

17. Draw the truth table for If.... Then or implication.

 p q 00 1 1 0 1 0 1 1 1 0 1

18. Draw the truth table for If and only If.

 p q 00 1 1 0 1 0 1 1 0 0 1

19. What are contingencies.

The propositions that have some combination of 1's and 0's in their truth table column, are called contingencies.

20. What are tautologies?

The propositions having nothing but 1's in their truth table column, are called tautologies.

The propositions having nothing but 0's in their truth table column, are called contradictions.

22. What is converse?

The converse of a conditional proposition is determined by interchanging the antecedent and consequent of given conditional. It results into a new conditional.

eg: Converse of .

23. What is inverse?

The inverse of a conditional proposition is another conditional having negated antecedent and consequent. That is the inverse of .

24. What is contrapositive?

The contrapositive of a conditional is formed by creating another conditional that takes its antecedent as negated consequent of earlier conditional and consequent as negated antecedent of earlier conditional. ie, contrapositive of .

25. Construct a truth table for the expression (A.(A+B)). What single term is the expression equivalent to?

 A B A+B (A.(A+B)) 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1

Looking at the table, we find that columns (A.(A+B)) and A are identical. That is, they posses the same truth set. Hence the given expression (A.(A+B)) is equivalent to A.

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