Discrete Math Exercises

Anonymous
timer Asked: Feb 26th, 2019
account_balance_wallet $25

Question Description

If a proof is given then label your variables, use proper algebra, and state a conclusion

2. Give P=1, Q=0, and R = 1what is S? 3. Write the negation and contrapositive for the following statement. x, y  R , if xy= 1 then one of the numbers is a reciprocal of the other. Negation: ___________________________________________________________________ Inverse:___________________________________________________________________ Converse:________________________________________________________________ Contrapositive: ____________________________________________________________ 5. Indicate whether the argument is valid or invalid. If valid then state which argument was used? If invalid then state which error was used? A) If compilation of a computer program produces error messages, the program is not correct. Compilation of this program does produce error messages. Therefore, this program is not correct. B) If the student is a freshman, then they must take writing. Caroline is not a freshman. Therefore, Caroline is not taking writing. 4. A set of premises and a conclusion is given. Use the valid argument forms to deduce the conclusion. a) q → r b) p → q c) ~ r 6. Let P(x) be the predicate “ x = d) ~ q  ~ p 1 ”. x a) Write P(2), P(1/2), P(-1), and P(-1/2) and determine the truth value of the statement. b) What is the domain of this P(x) if the x’s belong to all Real Numbers? 7. a. Represent the decimal integer 329 in binary notation. b. Represent 1001112 in decimal notation. 8. Determine whether the statement is true or false. Justify your answer with a direct proof or contradiction proof or a counterexample. If “a” is even integer and “b” is odd integer, then 3a2+ 2b2 is even. 9. Determine whether the following statements are logically equivalent by Supply a reason for each step. Prove: ~ (p  ~q)  (~ p  ~q)  ~p ~ (p  ~q)  (~ p  ~q)  (~ p  q)  (~ p  ~q) by __________________  ~ p  ( q  ~q) by_______________________ ~p (t) by_______________________ ~p by _______________________ 10. Which of the following sets are equal and why? A = {-1, -2,-3} B = {𝑥 ∈ ℝ| − 3 ≤ 𝑥 < 0} C= {𝑥 ∈ ℤ| − 3 < 𝑥 < 0} E= {𝑥 ∈ ℤ+ | − 3 < 𝑥 < 0} D= {𝑥 ∈ ℤ| − 4 < 𝑥 < 0} 11. Let C = D = {𝑥 ∈ ℤ| − 4 ≤ 𝑥 < 2} and define a relation S from C to D as follows: For all ( x, y )  C  D, ( x, y )  S , means that 1 1 − is an integer. Solve for the following. x y a. Is 2S5? ________ b. Is -1 S 1?________ c. Is 3 S 3?________ d. Write S as a set of ordered pairs._____________________________ e. Write the domain and co-domain. Domain:______________________ Codomain:_____________________ f. Draw an arrow diagram for S. 12. Determine whether the statement is true or false. Justify your answer with a direct proof or contradiction proof or a counterexample. “There is no greatest integer”

Tutor Answer

andythewxman
School: UIUC

Here you go. Please let me know if the...

flag Report DMCA
Review

Anonymous
awesome work thanks

Similar Questions
Hot Questions
Related Tags
Study Guides

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors