Let ⊕ denote the exclusive or, XOR, operation, defined by the following truth table. Construct a Boolean expression equivalent to P ⊕Q using only the connectives (func- tions) ∧, ∨, and ¬.

(IV) Give regular expressions for the following: L = {anbm | n ≥2, m <4} (i) Give two strings that are in the language. (ii) Give the regular expression for the complement of the above language.

For each of the following regular expressions over Σ = {a, b}, state 5 strings that are in the language of the regular expression, and 5 strings that are not.  1. (a∗b)∗|a∗2. (Σ∗aaΣ∗)|(Σ∗bbΣ∗)|(ab)∗|(ba)∗|a|b

2. Find a regular expression to describe the given language: { bc, b, abc, bс?, ..., а"bс, bc", ... }

Construct a regular expression and an FA defining the following language over Σ- (a, b). Explain your answer. - All words containing exactly two b's or exactly three b's, not more

Only if A and B are complement events (one is the complement of the other), it is true that P (AUB) = P (A) + P (B) True or false?

Find Disjunctive Normal Form of following expressions. Show the complete Process. (p ∨ ¬q) → q (p ∨ ¬r) ∧ (q ∨ ¬s)

Complete the truth table for the following expression showing work for each order of operation performed. p v q ^ r ^ ( p v r ) Is it a tautology, contradiction, or neither.  Explain why.

Consider the following regular expression over alphabet Σ = {a,b,c}:  Σ∗a+Σ∗bc Provide two strings that are in the language L and two strings that are not in the language L. w∈L: w∈L: w /∈L: w /∈L: