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- Question 4 Rewrite the following statement without using variables. Then, give an exam- ple that shows the statement is true. There exist two real numbers a and b such that ab > a + b. Question 5 Rewrite the following statement without using variables. Then, give an exam- ple that shows the statement is false. For any positive integer n, n³ > n².Tell if the statements are true or false. Let p: 2 + 1 = 3; q: 16 − 9 = 7. (a) ~p ∨ q TrueFalse (b) ~p ∧ ~q TrueFalse (c) ~(p ∧ q) TrueFalsePQ TT FT TF FF The definition of "P if and only if Q" (abbreviated Piff Q and symbolized as or ) is defined to be". Construct a truth table to show that "iff" means the same thing, as "has the same true value as". Be sure the explain how the truth table helps you answer this question.
- When the robot makes a turn, it would be useful to have an operation to perform on d to represent this turn. This is because after making a turn, the new value of d will depend on the old value of d. Complete the table for the new values of d if the robot is turning left or right.Then determine an expression in terms of d that will give the new position if the robot turns left and another expression if the robot turns right. Type these expressions in the last row of the table. Attached is the table I completed. All rows are correct except the last one. I'm not sure what my error is.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.Question 1: As you are a student of university now, you need to ensure your assignments are plagiarism-free. To do this, you decide to design a simple plagiarism checker. Your checker will take 2 strings as input. Then it will compare the 2 strings and check how many words they have in common. Then, print the percentage in common, by calculating: (No. of words in common / (No of words in string 1+ No of words in string 2)) * 100. If the calculated plagiarism is greater than or equal to 30%, print "Plagiarism detected." Otherwise, print "Good job!". Note: you need to compare "words" not individual characters. You can consider that all characters in both inputs will be in only lowercase or uppercase. ========= ======== Sample Input 1: my dog's name is bob bob is my dog's name Sample Output 1: Common percentage: 50% Plagiarism detected. Explanation 1: Length of string1= 5, Length of string2= 5, number of common words= 5. Hence, common percentage= (5/(5+5))*100 = 50 %3D Sample Input 2: my…
- Let B(x) = "x gets a biscotti". Which statements below mean "Either everyone gets a biscotti or no one gets a biscotti"? Select all that apply. Ox B(x) V-3x B(x) Ox B(x) V-Vx B(x) OV (B(x) V-B(x)) 03x B(x) → Vx B(x) 03x B(x) v Vx B(x)The equal sign ( = ) is used for testing equality. O True FalseSimplify the following Boolean expression: ? = ??′? + ??′?
- Can help me with the answer.Q11. Construct a truth table for the statements belowa. (p ∧ q) ∧ (~r ∨ q).b. ~[~p ∧ (q ∧ r)]c. [p ∧ (q ∨ ~p)] → ~p then find the truth value of the statement givena. p is a false statement, q is a true statement and r is a true statement.b. p is a false statement, q is a false statement and r is a false statement.c. p is a false statement, q is a false statement and r is a true statement.?Let M(x) = "x passed the midterm". Let F(x) = "x passed the final". Select the statement below which means: "If nobody passed the midterm, then everyone passed the final". Vx-M(x)→ VxF(x) Vx(M(x)→ F(x)). +VæM(z) → VF(x) Vx(-M(x) → F(x))