Conjunctive Normal Form
Question 1 
Which of the following is TRUE about formulae in Conjunctive Normal Form?
For any formula, there is a truth assignment for which at least half the clauses evaluate to true.
 
For any formula, there is a truth assignment for which all the clauses evaluate to true.
 
There is a formula such that for each truth assignment, at most onefourth of the clauses evaluate to true.
 
None of the above.

Question 1 Explanation:
For n=2, (means two variables a and b)
Formula: a ∧ b
Truth table:
Conjunctive normal form : (a ∨ b) ∧ (a ∨ ~b) ∧ (~a ∨ b)
Similarly,
For n=1TRUE=1, FALSE=1 (1/2 ARE TRUE)
For n=2TRUE=3, FALSE=1 (3/4 ARE TRUE)
For n=3TRUE=7, FALSE=1 (7/8 ARE TRUE)
(12^{n}) are TRUE.
Looking at options,
Formula: a ∧ b
Truth table:
Conjunctive normal form : (a ∨ b) ∧ (a ∨ ~b) ∧ (~a ∨ b)
Similarly,
For n=1TRUE=1, FALSE=1 (1/2 ARE TRUE)
For n=2TRUE=3, FALSE=1 (3/4 ARE TRUE)
For n=3TRUE=7, FALSE=1 (7/8 ARE TRUE)
(12^{n}) are TRUE.
Looking at options,
There is 1 question to complete.