Recent content by sapiental

Hey, thanks for the reply! I didn't put parenthesis around the ordered pairs (a,a),(b,b),(c,c) for the first problem, sorry. I don't think it's transitive since we have (c,b) and (b,a), and it doesn't contain (c,a). How does that sound? Thanks

Homework Statement relation A = {a,b,c} for the following matrix [1,0,0;1,1,0;0,1,1] is it reflexive, transitive, symmetric, antisymmetric Homework Equations ordered pairs. The Attempt at a Solution i wrote the ordered pairs as (a,a),(b,a),(b,b),(c,b),(c,c) I only that...

the problem states "assuming 10 friends consist of 6 single people and 2 married couples" sorry for not clarifying. would it still be off?

for c I did out all the cases case 1. where no married couples are invited, we have 6 friends for 5 spots = 6 different ways to invite case 2 one of the married couples for 2 spots, 6 singles for (6,3) = 20 different ways. since there are 2 married couples I multiply by 2 for a total...

Hi, thanks for all the input it really helped me gain more insight into the problem My new approach does not depend on the order and I employed the permutation and combination method. For a) I did C(10,5) = 10!/[(5!)(5!)] and got 252 possible combinations for b) i did the following C(2,1)...

Homework Statement a) if jack has 10 friends, in how many ways can he invite 5 of them to dinner. b) suppose 2 friends don't like each other, and if one is invited, the other can't come. c) what if 2 of the friends are married and if they invite that friend, the spouse must come. Homework...

Homework Statement How do I express t and s as functions of x and y given x = -(2t+1)*s/(t^2-1) y = e^(t + ln|s|) I keep getting stuck in a loop. Homework Equations substitution The Attempt at a Solution x= -(2t+1)*s/(t^2-1) I get t = sqrt(1-s/x) t = sqrt(1-s/x) s = e^(-t)y...

Homework Statement Compute the following double sum (n=3)(i=0)\sum(n=2)(j=0)\sum(3i+2j) Homework Equations sums The Attempt at a Solution my answer follows expanding the first sum, then just doing the last one i get (n=3)(i=0)[tex]\sum[tex](6+9i) = 78 thanks!

Homework Statement f: R -> R defined by f(x) = x^3 + 1 a) determine if it is one to one b)find its inverse c) calculate (f o f) Homework Equations if f(x) is one to one, if a = b, f(a) = f(b) The Attempt at a Solution a) yes it is because a^3 + 1 can't equal to b^3 +...

thanks!

Homework Statement Let A = {1,3,5,6}, B = {3,5} and C = {a,b,c} Compute a. A - B b. B x C (cartesian product) c. AB d. A(B-A) Homework Equations Table of set computation in text The Attempt at a Solution a. = {1,6} b. =...

Homework Statement a) How many bit strings are there of length 8? b) How many bit strings are there of length 8 which begins with 2 1's? Homework Equations Product Rule The Attempt at a Solution a) Since a bit string is either 0 or 1 there are two possibilities for each one...

Homework Statement Prove the following: If the integer n is divisible by 3 then n^3 is divisible by 3. Homework Equations Direct Proof The Attempt at a Solution n = 3m n^2 = 9m^2 n^2 = 3(3m^2) I think the proof is done at this point because the 3 factors out but I also...

Homework Statement Use logic to write the negation of the sentence: All participants of this course are IT majors and are Math majors (be careful, use basic logic laws) Homework Equations DeMorgan's Law The Attempt at a Solution Letting P(x) be Participants who are IT majors...

Homework Statement Hi, could someone please confirm my results. I just put my answers because the procedure is so long. let me know if you get the same results. 1) Wronskian(e^x, e^-x, sinh(x)) = 0 2) Wronskian(cos(ln(x)), sin(ln(x)) = 1/x * [cos^2(ln(x)) + sin^2(ln(x))] = 1/x thanks in...