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.
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A: Please refer to the following step for the complete solution of the problem above.
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A: Please refer to the following step for the complete solution of the problem above.
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- Scenario As you surely know, due to some astronomical reasons, years may be leap or common. The former are 366 days long, while the latter are 365 days long. Since the introduction of the Gregorian calendar (in 1582), the following rule is used to determine the kind of year: if the year number isn't divisible by four, it's a common year, otherwise, if the year number isn't divisible by 100, it's a leap year. otherwise, if the year number isn't divisible by 400, it's a common year. otherwise, it's a leap year. none of the above year int(input("enter the year")) if (year%4 1-0) and (year%400 -0) or (year % 1000): print (year is common year") else: print(year, is leap year") year= int(input ("enter the year")) if (years !-0) or (year480 1-0) and (year % 1001-0): print(year is common year") else: print(year, "is leap year") D year= int(input("enter the year"))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: 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]}
- Here are the choices for it to answerExercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…In a Chess match "a + b", each player has a clock which shows a minutes at the start and whenever a player makes a move, b seconds are added to this player's clock. Time on a player's clock decreases during that player's turns and remains unchanged during the other player's turns. If the time on some player's clock hits zero (but not only in this case), this player loses the game. N+1 There's a 3 + 2 blitz chess match. After N turns (i.e. moves made by 2 N white and moves made by black), the game ends and the clocks of the two 2 players stop; they show that the players (white and black) have A and B seconds left respectively. Note that after the N-th turn, b = 2 seconds are still added to the clock of the player that made the last move and then the game ends. Find the total duration of the game, i.e. the number of seconds that have elapsed from the start of the game until the end.
- (Translate the following argument into PL using letters to represent simple propositions as needed.) 1. All even numbers are divisible by 2, and all odd numbers aren't. A number n being odd implies that n is not divisible by 2. A number n is odd if an only i it is not divisible by 2. It can't be the the case that a number is both greater than 1 and not a prime number. Therefore, 3 is an odd prime number.Correct answer will be upvoted else downvoted. Computer science. You are given a positive integer x. Check whether the number x is representable as the amount of the solid shapes of two positive integers. Officially, you really want to check in case there are two integers an and b (1≤a,b) to such an extent that a3+b3=x. For instance, in the event that x=35, the numbers a=2 and b=3 are reasonable (23+33=8+27=35). In the event that x=4, no pair of numbers an and b is reasonable. Input The primary line contains one integer t (1≤t≤100) — the number of experiments. Then, at that point, t experiments follow. Each experiment contains one integer x (1≤x≤1012). Kindly note, that the input for some experiments will not squeeze into 32-cycle integer type, so you should use something like 64-bit integer type in your programming language. Output For each experiment, output on a different line: "Indeed" in case x is representable as the amount of the 3D shapes of two…Correct answer will be upvoted else downvoted. Computer science. You are given an integer n. Check if n has an odd divisor, more noteworthy than one (does there exist such a number x (x>1) that n is separable by x and x is odd). For instance, assuming n=6, there is x=3. Assuming n=4, such a number doesn't exist. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow. Each experiment contains one integer n (2≤n≤1014). If it's not too much trouble, note, that the input for some experiments will not squeeze into 32-cycle integer type, so you should use no less than 64-digit integer type in your programming language. Output For each experiment, output on a different line: "Indeed" if n has an odd divisor, more noteworthy than one; "NO" in any case. You can output "YES" and "NO" regardless (for instance, the strings yEs, indeed, Yes and YES will be perceived as certain).
- The user must be able to enter the information for a number of bookings from the keyboard. Ask whether a booking must be made (Y or N). If a booking must be made, a random 3 digit flight number must be generated. The user must be asked to enter the type of seat, the price per seat and the number of seats to book. Example of input:A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 10° F. After one-half minute the thermometer reads 57° F. What is the reading of the thermometer at t = 1 min? Assume that the rate of change of temperature in time is proportional to the difference between the thermometer's temperature and the air temperature. Type your answer in °F in the space provided below. Round your answer to two decimal places.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.