144 Answered Questions for the topic discrete mathematics

Axioms --> Clausal Form

Question :Consider the following sentences and prove that "Diana will win the game"1.All Players are clever.2.Anyone who is clever and dedicated can play the game well.3.Anyone who is playing the... more

Logic , Quantifiers , Logical Formula

Please note that I'll be using the following notations as follows, throughout the question.VX - For all X (Universal Quantifier)EX - For some X(Existential quantifier)Consider the logic formulas G1... more

Logic/Discrete Mathematics

Suppose one wishes to prove that "if all X are Y, then all Z are W". To do this, it would suffice to show that All Z are X, and all Y are W. All X are Z, and all W are Y. All Y are Z, and all W are... more

Discrete Mathematics - Logic

Could anyone explain what is the correct answer and why are the others are incorrect?Let P(x) be a property about some object x of type X. If we want to disprove the claim that "P(x) is true for... more

please make a significant effort to the problem and organized summary of the process you have followed and conclusions you can draw.

Five applicants are to be scheduled for job interviews at five given times. On an application form, each applicant was asked to mark two out of the five times. What is the probability that each of... more

how can I know all the probabilities

Five applicants are to be scheduled for job interviews at five given times. On an application form, each applicant was asked to mark two out of the five times. What is the probability that each of... more

I need a good explanation for this problem please

We’ll call a set of numbers un-average if the average of any two numbers in the set is not in the set. So {1, 3, 6, 7, 10} is un-average, but {1, 3, 6, 7, 9} is not. What is the largest set of... more

anyone can help me with this problem with some explanation

We’ll call a set of numbers un-average if the average of any two numbers in the set is not in the set. So {1, 3, 6, 7, 10} is un-average, but {1, 3, 6, 7, 9} is not. What is the largest set of... more

any idea in how to solve this ?

In a giant bin, we stir together 2019 red jelly beans and 2019 green jelly beans. We pull 3 jelly beans out of the bin at a time. There are two possibilities – they are all the same color or there... more

How am I supposed to show the predicate as true?

Given a while loop and a predicate. Show that if the predicate is true before entry to the loop, then it is also true after exit from the loop.predicate: m^3 > n^2 while (m ≥ 0 and m ≤ 100) dom... more

Prove or Disprove

(a) ∀a, b, c, m ∈ Z +, if a ≡ b (mod m), then c a ≡ c b (mod m). (b) For any positive odd integer n, 3|n or n 2 ≡ 1 (mod 12).

Prove or Disprove this statement

There exists a prime number x such that x + 16 and x + 32 are also prime numbers

Express statement in using quantifiers

I can see that it is straight forward when we have an statement like: "For all x, there exists a y, such that f(x,y) = 0", which I can re-write as: "∀ x ∃ y f(x,y) = 0". But, for example, when I... more

Intuition behind combination problem?

I came across this question on a GRE practice exam. I'm trying to build intuition behind how to correctly approach these types of problems: A reading list for a humanities course consists of 10... more

Intuition behind combination problem?

I came across this question on a GRE practice exam. I'm trying to build intuition behind how to correctly approach these types of problems: A reading list for a humanities course consists of 10... more

functions or not and surjective ,injective.

A2:={(x,y)∈R×R:x=y^3} I need to figure out whether it's a function or not and if it's I need to investigate if it's surjective or/and injective .I know ,that functions that give two outputs for a... more

I wanna to know the meaning of this ({a}∪{b})*

determine whether the string aabaa is in each of the following languages ({a}∪{b})* ..

Verify is tautology by using logical equivalence

Verify is tautology by using logical equivalence:((p ∨ q) ∧ (p → r) ∧ (∼ r)) → qby showing what law is using

In a conditional truth table( p -> q), why is that expression true, when p is false and q is true?

I am trying to understand truth tables and where they are derived from.

An urn contains eight red balls, eight white balls, and eight blue balls, and sample of four balls is drawn at random without replacement.

Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

Hard problem, discrete math.

If x+y+z=3 , x2+y2+z2=4, and x3+y3+z3=5 what is x, y, and z? I found that none of them can be equal or greater than 2.

Prove by Induction question, 2+6+18+...+ 2.3^n-1 = (3^n)-1

Can anyone help me solving this problem, Im really really lost. Thank you

Direct proof question, "The product of an even integer and an odd integer is even".

I didnt understand  Let say X = 2a +1 while y = 2b+1   Why you need to multiply xy rather x+y, as you can see below: XY = (2a+1)(2y+1) <- correct X+Y = 2a+1+2y+1 <- Incorrect   Can you... more

Counting / Permutation & Combination

Given two positive integers n and k with the same parity, count the number of sets S = { 0< s1 < s2 < ... < sk = n }, such that s1, s3, ... are odd numbers and s2, s4, ... are even numbers more
1 3 4 5 6

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