which of the following is a tautology? a.p+(qar) b. (pn q) →r с. (рлд) - (рvr) d. (pvr) → (pa g) O a O b d

For each statement below, decide whether it is true or false. If it is true, prove it. If it is not true, give a counterexample. All parts refer to languages over the alphabet {a, b}. (d) If neither L1 nor L2 can be accepted by an FA, then Lin L2 cannot.

The next 3 questions pertain to the following grammar from the book. The string to test is aba. S→ XY X→ XA | a | b Y→AY|a A→ a Question 1 Enter which variables can generate the following substrings of length 2 as found in stage 2 of the CYK algorithm. Enter no spaces. Enter multiple variables separated by a comma in alphabetical order (e.g., XY). If there are no variables that generate the substring, enter none. ab e ba e Question 2 Enter which variables can generate the following substrings of length 3 as found in stage 3 of the CYK algorithm. Enter no spaces. Enter multiple variables separated by a comma in alphabetical order (e.g., X,Y). If there are no variables that generate the substring, enter none. a ba e ab a +

For each statement below, decide whether it is true or false. If it is true, prove it. Ifit is not true, give a counterexample. All parts refer to languages over the alphabet {a, b}. (b) If Li C L2, and L2 cannot be accepted by an FA, then Li cannot.