Construct a truth table for the statement.
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- Rewrite the following statement formally. Use variables and include both quantifiers ∀ and ∃ in your answer. Every even integer greater than 2 can be written as a sum of two prime numbers.Complete the truth table below and answer the questions about the following argument: - (p → q) .'. r -(p → q) el b Row 1 Row 2 F Row 3 Row 4 F F Row 5 F T Row 6 F F Row 7 F Row 8 F F F (a) Which rows are critical rows? (Just put the row number, do not use spaces and separate each number with a comma. For example: "1,2,3,4") (b) Is the argument valid or valid/invalid? (Enter "valid" or "invalid") LLAnswer the following question in R and show the code.
- 4. ~(~C ≡ ~A) ѵ [(B ѵ C) • X] a) Replace each statement with the given assigned truth-values and rewrite the problem with the assigned truth-values ~(~t ≡ ~t) ѵ [(t ѵ t) • f] b) Using the truth-table, solve for the truth-value of the compound statementSolve the postfix expressions using appropriate data structures. 1. 456-*4/5 +6. Construct a truth table for the following argument to determine if it is valid. Work within the following grid. Is the argument Valid? Yes or No (circle one) ((p vq) ® -(p^)) :: -r+p
- Take an Infix expression from the user and convert into postfix. 1. Should be self-organizing program e.g. If the user enters two operators back to back by mistake. The program should automatically delete one of the 2 operators. 2. If the user doesn't enter a multiplication sign before a bracket, the program should automatically insert a multiplication sign there.Please write clearly, thank you1. (*) Find regular expressions to define the following tokens: string constants, boolean constants, hexadecimal numbers. 2. Write a regular expression that matches the following positive cases and does not match the following negative cases. Try to make the regular expression as general as possible. positive: 0, 10, 31, 1b, OB, 12x, 2aX, 1234567890, 11111000b, 123456789abcdefX, -0, -1b, -1bx negative: 00, 010, 31b, 1c, Od, xx, OcX, a, 2b, 3B, gX, -a, --1, 1-1 3. Translate the following regular expressions into one NFA: keywords: 0(12)*, number: [0123]+, special: 171? 4. Translate your NFA from task 3 to a DFA. Show all important steps. 5. Minimize the following DFA: a qo 6. (*) When you translate a regular expression to an NFA, and then to a DFA, and then minimize it - do you get a unique result? 7. (*) Translate the DFA from task 5 to a regular expression. Show all important steps. 8. Translate the following grammar to an NFA: A-> aB | bA | b, B-> aC | bB, C-> aA | bC|a 9. (*)…
- Determine whether the following argument is valid or invalid. type a truth table and a few words explaining why the truth table shows validity or invalidity. If 12 divides 709,438 then 3 divides 709,438. If the sum of the digits of 709,438 is divisible by 9 then 3 divides 709,438. The sum of the digits of 709,438 is not divisible by 9. Therefore, 12 does not divide 709,438.TRUE OR FALSE:1.) All prime implicants are essential and must be included in the final Boolean expression.2.) Only a maximum of 3-cube is allowed in Tabulation Method.3.) Don't care conditions are included in the Prime Implicant table in determining the Essential Prime Implicants.Evaluate the following expressions. (3,4)