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254 Answered Questions for the topic logic


Probability - Thank you for answering

thank you very much for the help!
Logic Math Algebra


What is the sum of the 1001st to 1006st digits of the decimal representation of 1/13 ?

What is the sum of the 1001st to 1006st digits of the decimal representation of 1/13 ?


Very difficult probability problem More help would be appreciated! - What is the probability that at least one attendee is on the call with everyone else?

One Friday morning, suppose everyone in the U.S. (about 330 million people) joins a single Zoom meeting between 8 a.m. and 9 a.m. This being a virtual meeting, many people will join late and leave... more


Show that |= ∃x (Dx → ∀x Dx).



first-order logic of the following sequence

“There is a barber in Atlantis who shaves exactly those citizens of Atlantis who do not shavethemselves. Therefore, there is a barber in Atlantis who is not a citizen of Atlantis.”Parameters: ∀; B,... more
Logic Maths Trick


Find x,y ? If xto the power y is equal to the y to the power of x and given x not equal to y?

GivenXy=yxX not equal to y


Show that {α ∨ β, ¬α} ⊢ β.

α, β are well formed formulas


A real doozy - which situation produces the highest expected roll?

The fifth edition of Dungeons & Dragons introduced a system of “advantage and disadvantage.” When you roll a die “with advantage,” you roll the die twice and keep the higher result. Rolling... more
Logic Math


Mathematical Logic Problems

1.Let A and B be sets in a universe U. Prove that the following equality holds:(A∪B)−(A∩B) = (A−B)∪(B−A)2.Let a1, a2, ··· be a sequence of real numbers.We say lim n→∞ an = 11 if for all ∈ > 0,... more
Logic Math


In need of a tutor for this type of questions?

 { D→(A∨¬C), ¬B→(D∨C), ¬A→¬(B∧C), (B∨D)↔C } ⊢A
Logic Math Calculus


Rules of Inference Validity

I'm confused in the equations. Can you help me to find this validity using rules of inference methods or resolution principle?
Logic Math Algebra


(a) What percent of the people surveyed owned a cell phone? (b) What percent of the people surveyed owned only a cell phone?

A consumer survey was conducted to examine patterns in ownership of tablet computers, cellular telephones, and Blu-ray players. The following data were obtained: 317 people had tablet... more


Proof by natural deduction

1. (~F v X) ↄ (P v T) 2. F ↄ P3. ~P /T

Sentential Logic Question: Translating "at most"

B: Barack will make it to the top of the peakD: Dallas will make it to the top of the peakA: Anise will make it to the top of the peakR: Rod will make it to the top of the peakBetween Barack,... more


Translating the following statement in FOL

“A number x is composite (P(x)) if and only if x is divisible by some number y (Q(x, y)) other than 1 or itself, and x is not composite if and only if there does not exist any number y such that y... more


Why do our fingers have finger-tips but our toes dont have toe-tips

Logic Logic Pro


Logical Analysis

Six friends are sitting in a rectangular table with 6 seats, one at the head of the table, and two on each long side of the table. The chairs are numbered from 1 through 6 in a clockwise manner,... more
Logic Algebra Proofs


How can i show and prove rigorously that for all integers, i can paint all these segments red?

Three counters, A, B, C are placed at the corners of an equilateral triangle of side n. The triangle is divided into triangles of side length 1. Initially all lines of the figure are painted blue.... more


Show that (p↔q)≡(p∧q)∨(¬p∧¬q) using equivalence laws.

Can you give the answer step by step? Need answer ASAP in one hour


Mathematical Reasoning

I can't understand the answers provided for these 2 question in a textbook:Question 1 : State whether true or false a) Implication : If 4 is a root of x2 - 16 = 0, then 4 is not a root of ( x +... more


How would we express the relative probability given odds ratios in this problem?

Hypothetical scenario:Given: In a population, we know there are 3 people who have a car for every 5 people who have a scooter. There are also people who have a bicycle; but we do not know about... more


Assume also that you make ONLY the minimum payments. Determine when the balance drops below $200?

You have a balance of $4000 on your credit card, and you make no more charges. Assume that the card requires a minimum payment of 5% and carries an APR of 22.8%. You have a balance of $4000 on your... more
Logic Philosophy


Help sought to solve ~(A&B) / ~(A&~B) // ~A

A student contacted me asking for assistance in validating this symbolic logic (propositional) argument:~(A&B)~(A&~B)~AThe question required the use of the Assumed Indirect Proof method,... more


Negation of A and B

a) Los Angeles is a city of Texas b) If I am in Houston then I am in Texas.


Mathematics IT (Discrete Structures)

For items 31 – 34. Fill in the blanks with word to complete the statement.a. Negation                     b. Tautology            c. Aristotle        d. Premise 31. The father of logic... more
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