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Discrete Math 2. (a). Rewrite the following statement in equivalent if then form. Either 2021 is...
answer a through e. Topic: Discrete Math
Hw w2_p4 The notationョ! stands for the words "there exists a unique" or "there exists one, and only one," or "there exist exactly one." For example, consider the following multiply quantified statement, a. Is the statement true or false? If it is true, what is e? If it is false justify your conclusion. b. Rewrite the statement as an equivalent statement that does not use 3!. c. Negate the universal statement, (Be careful;...
2. For the following quantified statement, (a) Write the negation of the statement. (Don't simply put a in front of the statement. Actually rewrite to get a quantified statement that is equivalent to the negation.) Original Statement: Vr e Z. By e Z, az eZ: 72 = y2 + z2. Negation of the original statement: (b) Decide whether the original statement is true or the negation of the original statement is true. Include some brief justification of how you know.
3. (10pt) Consider quantified statement For every meS and n ES, mn – 2 is prime. where the domain of the variables m and n is S = {3, 5, 11}. (a) Express this statement in symbols. (b) Is the quantified statement in (a) true or false? Explain. (c) Express the negation of the quantified statement in (a) in symbols. (d) Express the negation of the quantified statement in (a) in words. (c) Is the negation of the quantified statement...
Rewrite the following switch statement as an equivalent if statement. The variable digit is of type int. switch (digit) { case 0: case 1: value = 3; break; case 2: value = 6; break; case 3: value = 9; break; default: value = 0; }
Discrete math
DQuestion 6 Consider the following statement: If a s b mod 5 and ab mod 2 then a b mod 100 Which of the following is true about this statement? O The statement is true. . The statement is false
Discrete Math Answer all questions on another sheet of paper. You do not need to print out or recopy the questions. Please skip lines and write legibly. Reading Worksheet-Sections 2.1 and 2.2 1. s the sentence below a "proposition"? Why or why not? Maurice is enrolled in Discrete Math this semester. 2. Let p: "Arnold likes to read science fiction." Let q: "Arnold is a baseball player." a) If p is false and q is true, what can you say...
Discrete math 1 1) In RSA algorithm, suppose the public key n = 55 (11*5) and e = 17. Please find a private key d which ed = 1 (mod 40) (40 = (11-1)(5-1)) 2) From the previous problem, suppose we have a message "one" (Letter A to Z are coded as 00 to 25), what will be the ciphered message? 3)Rewrite the classic Binary Search method as a Recursive Function (just the pseudocode.) 4)Deduce that, if A ⊆ B,...
Discrete Math
Give a big-Theta estimate for the number of additions in the following algorithm a) procedure f (n: integer) bar = 0; for i = 1 to n^3 for j = 1 to n^2 bar = bar + i + j return bar b) Consider the procedure T given below. procedure T (n: positive integer) if n = 1 return 2 for i = 1 to n^3 x = x + x + x return T(/4) + T(/4) +...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
Discrete Math
11. Consider the function f : ZZ, given by f(n) = 5n - 2. (a). Show that f is injective (namely, one-to-one). (b). Determine if f is surjective (namely, onto). Justify your answer.