Use a truth table to determine whether the two statements are equivalent. ~(q→p) and q ~P
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- Let p be the statement "I celebrate" and q be the statement "Bangladesh wins". [Hint: The following statements express p→q:“if p, then q”, “p implies q”, “if p, q”, “p only if q”, “only if q, p”, “p is sufficient for q”, “a sufficient condition for q is p”, “q if p”, “q whenever p”, “q when p”, “q is necessary for p”, “a necessary condition for p is q”, “q follows from p”, “q unless ¬p”] d)Which of the following expresses inverse of p→q?. 1. Bangladesh loses whenever I am sad. 2. Only if I am sad, Bangladesh loses. 3. Bangladesh loses only if I am sad. 4. A necessary condition for Bangladesh to lose is my sadness.Let p be the statement "I celebrate" and q be the statement "Bangladesh wins". [Hint: The following statements express p→q:“if p, then q”, “p implies q”, “if p, q”, “p only if q”, “only if q, p”, “p is sufficient for q”, “a sufficient condition for q is p”, “q if p”, “q whenever p”, “q when p”, “q is necessary for p”, “a necessary condition for p is q”, “q follows from p”, “q unless ¬p”] The following four questions are all based on the paragraph above. You have to answer all of them in order to be able to click the submit button down below. a) Which of the following expresses p→q?. 1.Bangladesh wins whenever I celebrate. 2.Only if I celebrate, Bangladesh wins. 3.Bangladesh wins only if I celebrate. 4.A necessary condition for Bangladesh to win is my celebration.Write the following compound statement in terms of the simple statements p, q, and r. "I go to office hours and ask questions, and my professor does not remember me." p: I go to office hours. q: I ask questions. r: My professor remembers me.
- 10. Let p be the statement “He gets frustrated.” and q be the statement “He will be able to complete the job.” Translate ~(p ∧ q) into the equivalent statement.In C++ 1. Declare, define, and test the following function to check for order by name:bool isSortedByName(const Student * sa, int size);2. Declare, define, and test the following function to check for order by ID:bool isSortedById(const Student * sa, int size);3. To print out a Boolean value as true or false, rather than 1 or 0, precede each with boolalpha:cout << "True is " << boolalpha << true << ", False is " << boolalpha << false <<endl;Let p, q, and r represent the following statements: p: The first ball is red. q: The second ball is white. r: The third ball is blue. Which would be the correct English statement for the symbolic form (¬¬p ∧∧ q) →→ r ? Group of answer choices A .If the first ball is red or the second ball is white, then the third ball is blue. B. If the first ball is not red or the second ball is white, then the third ball is blue. C .If the first ball is not red and the second ball is white, then the third ball is blue. D. If the first ball is red and the second ball is white, then the third ball is blue.
- please do the following in c++ A school has 100 lockers and 100 students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S1, opens every locker. Then the second student, S2, begins with the second locker, denoted L2, and closes every other locker. Student S3 begins with the third locker and changes every third locker (closes it if it was open, and opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker. Student S5 starts with L5 and changes every fifth locker, and so on, until student S100 changes L100.After all the students have passed through the building and changed the lockers, which lockers are open? Write a program to find your answer and display all open locker numbers separated by exactly one space.(Hint: Use an array of 100 bool elements, each of which indicates whether a locker is open (true) or closed (false). Initially, all lockers are closed.)1. Let p, q, and r be the statementsp: I finish my assignment before 2:00 pm todayq: I go to the gym todayr: It is raining today (a) Invent a compound statement that uses all three of the proposi-tions p, q, and r as well as whatever logical connectives you choose. (b) Write an English sentence that corresponds to the statement youconstructed in (a). (c) Make a truth table for the statement you constructed in (a).use c++ to answer the folloing question in an ancient land, the beautiful princess Eve had many suitors. She decided on the following procedure to determine which suitos she would marry First, all of the sustors would be lined up one after the other and assigned numbers. The first suitor would be number 1, the second number 2, and so on up to the last suitor, number a. Starting at the first suitor she would thes count three suitors éown the line (because of the three letters in her name) and the third suitor Would be eliminated from winning her hand and removed from the line. Eve would then continue, counting three more suitors, and eliminating every third suitor When she reached the end of the line she would contmpe counhng from the beginning. For example, if there were 6 suitors then the elimination process would proceed as follows: 123456 initia! list of suitors, start counting from 1 12456 suitor 3 eliminated, continve counting from 4 1245 sustor 6 eliminated, continue counting…
- Considering p, r and q are statements, use logic laws to indicate: (pvq) →r ≡ (p→r) ᴧ (q→r) By using logic laws, determine if the statement below is a contradiction, tautology or neither. [p→(q→p)] ↔ (pᴧ¬p) By using logic laws, test if the argument below is valid: Either I exercise regularly, or I eat healthy. If I exercise regularly then I will not get fat. I got fat. Therefore, I am healthy.Question: 1A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself). For example, 6 is a perfect number. The divisors of 6 except itself are 1,2 and 3. The sum of the proper divisors of 6 is 6. Thus 6 is a perfect number. You have to take integers as input and continue taking input until the word “STOP” is given as input. After taking the inputs you have to classify the integers as Perfect and Imperfect and store it in a dictionary(Please see the output for better understanding).[Note: You CANNOT use any built in functions EXCEPT input(),range(),print()]Sample Input :61082528100496530STOPSample Output:(No need to follow the output format. Just print the resultant dictionary.){Perfect: [6,28,496],Imperfect: [10,8,25,100,530]}Modified coin-row problem:If we modified the coin-row problem, so that you cannot take the adjacent coin, and youcannot take the coin next to the adjacent coin also (see example below), what would thedynamic programming formula F(n) be?Example: A, B, C, D, E, F, G, H, I, JIf A is taken, then B & C cannot be taken, but D (or above D, like E and so on) can be taken.If B is taken, then A, C, D cannot be taken.And so on.