In a few sentences, discuss the differences in approach to these two statements, in the context of quantifiers ( "for all - inverted A and " there exists -inverted E) STATEMENTS: “If n is an odd integer, then n^2-n is even" and "prove or disprove the following if n is an odd integer, then n^2-n is odd"
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In a few sentences, discuss the differences in approach to these two statements, in the
context of quantifiers ( "for all - inverted A and " there exists -inverted E)
STATEMENTS: “If n is an odd integer, then n^2-n is even" and "prove or disprove the following if n is an odd integer, then n^2-n is odd"
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- Let P(n) be the statement that a postage of n cents can be formed using just 4-cent and 5-cent stamps." Use strong mathematical induction to prove that P(n) is true for n ≥ 12. Answer the following questions to show a complete proof (Please remember that you must prove the statement using strong mathematical induction) Show that the statements P(12), P(13), P(14), and P(15) are true, completing the basis step of the proof. What is the inductive hypothesis of the proof? What do you need to prove in the inductive step? Complete the inductive step for k ≥ 15.Write a formal proof for the following biconditional statement.For all integers n, n^3 is even if and only if n is even.[Hint: For one of the two directions of this proof, you might want to consider a proof using the contrapositive.][Reminder: You may use the parity property, which states that each integeris either even or odd, but not both.]9. Let m, n are integers. Use a proof by contraposition to prove that if m*n is even, then m is even or n is even. 10. Let n be an integer. Use a proof by contradiction to prove that if 3n+2 is even, then n is even.
- 4. Let P be the statement "If n´ is an odd integer, then n is odd integer." (a). What is the contraposition of P? (b). Prove P by contraposition.Write a formal proof of the following statement. Be sure to copy this statement on your paper before beginning the proof. For all integers n, n is even if and only if 3n is even. Note: An "if-and-only-if" statement requires that you prove both implications: "if n is even then 3n is even" and "if 3n is even then n is even."The Problem A Zeckendorf number is defined for all positive integers as the number of Fibonacci numbers which must be added to equal a given number k. So, the positive integer 28 is the sum of three Fibonacci numbers (21, 5, and 2), so the Zeckendorf number for k = 28 is three. Wikipedia is a satisfactory reference for our purposes for more details of the Zeckendorf and Fibonacci numbers. In both cases, you do not need to read the entire Wikipedia entry. Your assignment is to write two ARM assembly language functions which calculate Zeckendorf and Fibonacci numbers. Zeck function The first function, which should be named zeck, receives an integer parameter in register zero. This will be the variable k we discussed above. Your code should return the Zeckendorf number for k in register zero when complete. If the parameter k is zero, return zero. If the parameter k is negative, return minus 1. If the parameter k is too large to calculate, return minus 1. Fib function The other function,…
- 6 7 8 9 10 ======= 11 12 13 14 15 16 17 18 19 20 21 22 XO la b 1 m Periodicity U 50 33 97 D XI E F G H I J L M N Use linear congruential generator approach to find Xi, what is the periodicity? Rename cells C4, C5, C6 and C7 as X0, a, b and m, respectively. RUDIMENTS OF RANDOM NUMBER GENERATION (1 OF 2) LINEAR CONGRUENTIAL GENERATORS (BYLEHMER 1951 A sequence of integers defined by the following recursive formula X = (ax +b) MOD m, 1 = 0, 1.... which means divide (ax, + b) by m, let X... be the remainder of this division a multiplier b increment m the modulus x0 seed or initial point 0 PProve each of the following statements. 6 divides n3 – n whenever n is a nonnegative integerIf n is an integer, what are the common divisors of n and 1? What are thecommon divisors of n and 0?
- Correct answer will be upvoted else downvoted. Computer science. Positive integer x is called divisor of positive integer y, in case y is distinguishable by x without remaining portion. For instance, 1 is a divisor of 7 and 3 isn't divisor of 8. We gave you an integer d and requested that you track down the littlest positive integer a, to such an extent that a has no less than 4 divisors; contrast between any two divisors of an is essentially d. Input The primary line contains a solitary integer t (1≤t≤3000) — the number of experiments. The primary line of each experiment contains a solitary integer d (1≤d≤10000). Output For each experiment print one integer a — the response for this experiment.3. Two 7-digit integers (leading zeros allowed) are considered to be equivalent if one can be obtained from the other by rearranging its digits. For example, 0012234, 0312042, 3220014 and 2100243 are all considered equivalent, whereas 0012234 and 0001234 are not equivalent. How many nonequivalent 7-digit integers are there in which the digits 0, 2, 4 and 6 can each appear at most once?2- Prove that the following statements are true (7) or false (F). (let log n = log2 n). You must define first what you are trying to prove using the limit definition. a) n³/log n = O(n), for any integer constant 2 ≤ k ≤ 3. E b) n+nlog n = (n log n), for any positive integer constant k. c) n log n² = Q(), for any integer constant k> 0.