Complete the following direct proof of the statement: If x and y are positive real numbers and x < y, then x² < y². Hint: answer each blank with an expression. Type "x^2" for "x2". proof. Since Since Since x² < , multiply both sides of x < y by x yields , mutiply both sides of x < y by y yields <²₁x² < y².0
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- 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.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.True or False? The expression ! (x > 0) is true only if x is a negative number.
- Evaluate the following expressions and determine the value of allvariables, based on the above variable declarations.Correct answer only. Code and output screenshot. Nastia has 2 positive integers An and B. She characterizes that: The integer is acceptable in case it is detachable by A⋅B; In any case, the integer is almost acceptable, in case it is detachable by A. For instance, if A=6 and B=4, the integers 24 and 72 are acceptable, the integers 6, 660 and 12 are almost acceptable, the integers 16, 7 are neither acceptable nor almost great. Discover 3 unique positive integers x, y, and z to such an extent that precisely one of them is acceptable and the other 2 are almost acceptable, and x+y=z. Input The main line contains a solitary integer t (1≤t≤10000) — the number of experiments. The primary line of each experiment contains two integers An and B (1≤A≤106, 1≤B≤106) — numbers that Nastia has. Output For each experiment print: "Indeed" and 3 distinct positive integers x, y, and z (1≤x,y,z≤1018) to such an extent that precisely one of them is acceptable and the other 2…Write the form of the following argument. Is the argument valid or invalid? Justify your answer. type the truth table on the space provided below. If 54,587 is a prime number, then 17 is not a divisor of 54,587. 17 is a divisor of 54,587. Therefore, 54,587 is not a prime number.
- TRUE OR FALSE. Write TRUE if the statement is true, otherwise, writeFALSE.If P and Q are true statements and R is a false statement, then the statement (P ∧ Q) ∨ R ⇒ (¬Q) is true.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"))An argument is expressed in English below. Rhys will go to the beach. If Rhys is excited; then Rhys will go to the beach. Rhys is excited. Variable names are assigned to each English phrase as follows: p: Rhys is excited •q: Rhys will go to the beach Is the argument valid? If valid, then indicate which rule is used for the argument. If invalid, then give truth assignments to the variables that prove the argument is invalid. Pick 4. Check Next