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If f is injective, while both f ◦ g and f ◦ g0 are defined, show that f ◦ g = f ◦ g0 =⇒ g = g0.
It is defined as,
Step by step
Solved in 2 steps
- Find the most general unifier (if it exists): a) Marries (x, John), Marries (Elizabeth, y) b) Marries (thatperson, Mary), Marries (father (Me), mother (y))Give at least one example of injective, surjective and bijectiveIn the WHILE language, prove that if <while b do y := y-x,s> ⇓ s' then there exists an integer k such that s(y) = s'(y) + k * s(x) Please use induction on derivations, with induction hypothesis.
- The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(%%1%%2%%3%%4)?Suppose P(a) is the predicate "a is prime" and Q(a) is the predicate "a is divisible by 3", for all integers a. In the following, the domain is the set of integers. What is the truth value of ∃x(P(x)∧Q(x))? Justify your answer.Expand on the concept of Black Box and then go into detail on primivitive functions:
- (a) For each of the following regular expressions, draw a deterministic finite automaton that recognises the same language. (ii) (a+b)(a+b+0+1)*@(a+b)(a+b)*.(a+b)(a+b)*Let ∑ = {a, b}. Solve the following questions: Given a regular expression r=(bb^* a+aa^* b)^*, find an NFA to accept the language L(r).1- let p,q and r be propositions. Simplify the following compound proposition: ((¬ r)∧p∧q)∨((¬ r)∧(¬ p)∧q). 2 - Using two different methods determine whether the propositions (p⟶q)⟶q and p∨q are logically equivalent.
- Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF {wct | t ∈ {a,b}* ∧ w is a substring of t}Let α = (a + b)∗ab(a + b)∗. Give a regular expression equivalent to ∼ α in the following cases.Simplify the expressions as much as possible (either using the rules from the lecture or othermeans).(a) Σ = {a,b}(b) Σ = {a,b,c}Automata and ComputabilityList all eight well-formed sentences of TFL that are sub-sentences of the followingsentence. ¬(P → (R ↔ (S ∨ T)))