Ask Ghassem - Recent activity in Discrete Mathematics

Probability of a bus arrived in its destination based on weather condition

Mon, 09 Nov 2020 13:06:47 +0000

A bus is making its way to a destination. If the weather conditions are favorable today, the likelihood of delay is 3%. If the weather conditions are not favorable today, the likelihood of delay is 50%. The forecast predicts that it is 20% likely that the weather conditions will be favorable today.

1. What is the likelihood that the bus will be delayed?

2. The bus has arrived, but it was delayed. Given that the bus was delayed, what is the likelihood that the weather conditions were favorable?

Commented: How can I prove that following is a tautology (using laws of logical equivalences)

Tue, 18 Feb 2020 19:50:20 +0000

If you can record a video, and explain step by step, that would be much better. It could be confusing how you conclude line 6 from line 5, but if you just record a video and talk over it while solving, that will be clarified. In addition, I removed your personal information such as student number from your post. Please do not include them while posting publicly.

Answered: can someone send me an online link to discrete mathematics 8th edition textbook?

Thu, 13 Feb 2020 15:27:35 +0000

I think this link is what you want. However, it is better you purchase the book

Understanding symbolic language of problem, quantificational logic

Sun, 26 Jan 2020 11:18:05 +0000

Hi, i am having trouble interpreting the information contained in the relation R, and how it should be applied to the Ps in this problem:

Consider the formula

∃x∃y∃z(P(x,y)∧P(z,y)∧P(x,z)∧¬P(z,x))

Under each pf these interpretations, is this formula true? In each case, R is the relation corresponding to P.

(a) U = N, R = {<x,y> : x<y}.

(b) U = N, R = {<x,x+1> : x≥0}.

Does <x,y> refer to the variables x,y or z in each P(a,b), and the :x<y refer to what the relation between these two should be?

I tried something like this for (a) and got:

∃x∃y∃z((x<y)∧(z<y)∧(x<z)∧¬(z<x))

However I'm not sure if this is correct, and I'm not sure how I would do it for (b)

Answer selected: What are the values stored in tc8 format for the following numbers?

Fri, 24 Jan 2020 01:02:27 +0000

Q1-ANS)
for -117d:

    $-117d = -(01110101)b$

    $-(01110101)b = 10001010(oc8) + 1 = 10001011(tc8)$

for -127d:

    $-127d=-(01111111)b$

    $-(01111111)b = 10000000(oc8) + 1 = 10000001(tc8)$

for 127d:

    $127d = 01111111b = 01111111(tc8)$

for 0d:

    $0d = 00000000b$

    $Two's complement = one's complement + 1 = 11111111(oc8) +1 = 00000000(tc8)$

    due to overflow the 9th digit is removed

Q2-ANS)

    1.

    $10010001(tc8) = -(01101110+1)d = -(01101111)b = -((0 × 2^7) + (1 × 2^6) + (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (1 × 2^2) + (1 × 2^1) + (1 × 2^0))d = -111d$

    2.

    $00010001(tc8) = ((0 × 2^6) + (0 × 2^5) + (1 × 2^4) + (0 × 2^3) + (0 × 2^2) + (0 × 2^1) + (1 × 2^0))d = 17d$

    3.

    $01111111(tc8) = ((1 × 2^6) + (1 × 2^5) + (1 × 2^4) + (1 × 2^3) + (1 × 2^2) + (1 × 2^1) + (1 × 2^0))d = 127d$

    4.

    $0000000 (tc8) = ((0 × 2^6) + (0 × 2^5) + (0 × 2^4) + (0 × 2^3) + (0 × 2^2) + (0 × 2^1) + (0 × 2^0))d = 0d$

    5.

    $11111111(tc8) = -(00000000 + 1)b = -(00000001) = -1d$

Answer submitted by Amirhossein Azizafshari from Thursday 1 PM class.

Answer selected: How do i find the inverse of the function?

Fri, 06 Dec 2019 04:35:19 +0000

Hey there bro. Let me teach you a trick to solving simple inverse functions. Let's use your question as an example. Let's switch the x and the y. This will give us $x = 4y + 5$. Now try and isolate the y again. You should end up with $y = (x-5)/4$. have fun!

Answer selected: How to calculate $g[h(3)]$ if $g(x)= 2x+3$ and $h(x) =4x+5$ ?

Fri, 06 Dec 2019 04:35:09 +0000

You need to calculate $h(3)$ first. $h(3)= 4\times3+5=17$.

Therefore, $g[h(3)]=g(17)= 2\times17+3=37$.

Answered: Can anyone please solve Q7 pg 329 in Induction?

Thu, 05 Dec 2019 22:10:12 +0000

Never mind, I was able to solve it myself. The trick was rearranging and factoring $5^{k+1}$ and add exponents to get $5^{k+2}$.

Answer selected: Could you please share a good cheat sheet for logic gates?

Fri, 15 Mar 2019 17:38:23 +0000

Please take a look at the following table that contains most common logic gates and their truth tables. You can download it by clicking on it.

Answered: What's the differences between [NOT p OR NOT q] and [NOT (p OR q) ]

Fri, 12 Oct 2018 19:07:35 +0000

p	q	not p	not q	not p or not q	p or q	not(p or q)
T	T	F	F	F	T	F
T	F	F	T	T	T	F
F	T	T	F	T	T	F
F	F	T	T	T	F	T

I write a truth table about the question, you can find that [NOT p OR NOT q] and [NOT(p OR q)]are different.

Answered: Could you please share cheat sheet of Logic Operations?

Mon, 08 Oct 2018 17:52:18 +0000

You can download the pdf version from here.

https://i.imgur.com/B7fBkWJ.png
https://i.imgur.com/9bd62ba.png

Answered: What does verifying message integrity have to do with boolean simplification and truth tables?

Sat, 06 Oct 2018 13:49:31 +0000

The message is considered as "corrupted" if in the destination we do not have the same message. The question is quite simple I believe. Do not overthink :-)

Commented: What is the priority order of Either Or (EOR) when constructing truth tables

Thu, 04 Oct 2018 14:02:45 +0000

So I believe I found the order, and it turns out the XOR is in between AND and OR, it can be shown in precedence order 8,9 and 10, in the following link
https://en.cppreference.com/w/c/language/operator_precedence
Thank You.

Commented: Is this answer to a question counted as a legitimate answer

Thu, 04 Oct 2018 13:54:39 +0000

Well I did have another solution which is the following,

NOT(p OR NOT q) OR NOT(p OR NOT q)

I feel like this would be a better answer, but I still have the same concern as of the first one

Retagged: Is there any easy way to draw the Truth Table for logic expressions?

Tue, 02 Oct 2018 16:32:36 +0000

I can solve the Truth Table, but do not know how to verify my answers. Could you please suggest a tool for it?

Answered: Where can I find the solution manual for Discrete Mathematics and Its Applications by Rosen?

Fri, 28 Sep 2018 17:18:31 +0000

I just searched in Google and I found these two links to the book and to its solution manual. If the links are broken, try to search for them!

Answer selected: How can I convert between binary/hexadecimal numbers with decimals into a decimal number system

Thu, 27 Sep 2018 05:45:33 +0000

I have written the procedure down, please click the link

https://imgur.com/gallery/2N4eqBb

And you can also click the links of WolframAlpha below to check the answers

011010.011 in binary to decimal

1C0DE.4A base16 to decimal

Edited: Where can I find some good Numbering System Exercises and learning it better?

Sun, 16 Sep 2018 01:53:44 +0000

I have a math course at College and I am wondering if someone can show me resources I can use to improve my math skills in discrete math, especially for Number Systems?