If A⋂B are independent, prove that Ac⋂B are independent.

Q: Show that if a|b then -a|b.

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Q: Prove that: 1- Ā. (B × C) = B . (Č × Ā) = C . (Ā × B)

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Show that for baetween ( tana

A: Show that for x between π4,1 for the function tanxx=32.

Q: Prove that neQ

A: Given ddxxn=nxn-1

Q: Prove that AAB = (AU B) - (An B),

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Q: (2) (a) Show using set identities that AUBU(AN BNT) = AUBUT (b) Prove by contradiction that if A C…

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Q: ) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.

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Q: Prove that. E) define and give example

A: 1. Binary operation 2. Idempotent element 3. Odd permulation 4. Cyclic group

Q: How to prove that a formula A is valid iff ¬A is unsatisfiable?

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Q: An element x is in A ∪ B if, and only if, _____________________.

A: Known fact: A∪B=x | x∈A or x∈B

Q: Prove: If a > 0, then (1/a) > 0.

A: It is given that a> 0.It is known that if ab > 0 then a > 0 or b > 0 or a< 0 or b…

Q: If a,b,c,d are in continued properties,prove that

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Q: Let feC-2,2], fo-o. Prove that Max -2

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Q: Use proof by contradiction to prove that if x + y > 2, then x > 1or y > 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: Let S be the s

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Q: Prove that ABC and EDC are similar

A: In triangle ∆ABC we have given  AB=3, BC=5 and CA=4In triangle ∆EDC we have given  ED=9, DC=15 and…

Q: Prove or disprove the following statement: for all x € R, [x] = –[-x]

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Q: Cing theN

A: Given limit is,limn→∞6n2-2n+12n2+1

Q: If A =I then what is A'?

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Q: Prove that (An (BUC)) = AU BUC.

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Q: Give an example of a closed subset S of R^2 such that conv S is not closed

A: An example of a closed subset S of R2 such that conv S is not closed is given below.

Q: Use the given information to prove that ADEF ADGF.

A: We need to find out the reason and complete the proof .

Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

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Q: Prove that if ACØ then A = (Ø.

A: To prove the given statement.

Q: ns of this assertion.

A: Exact differentials : Recall that change in internal energy , dv ,is called an exact differential…

Q: Let Σ be a set of well formed formulas and α, β be well formed formulas. Show thatΣ ∪ {α} |= β if…

A: If Σ⊨(α→β), and (Σ∪{α}) holds, then both Σ and α hold (a set is only true if every member of the set…

Q: Use set identities or different proof method to show that: (A U B) n (B U A°) = B

A: To prove A∪B∩B∪Ac=B If A and B both are empty sets φ, then there is nothing to prove. If A=φ, B≠φ,…

Q: Prove A by Contradiction

A: Solution :-

Q: State and Prove Pick’s Theorem.

A: Let P⊂ℝ2 be a polygon with all vertices on lattice points on the grid Z2. Let  I be the number of…

Q: Prove: | ab | = | a | * | b | for all a's and b's in the reals.

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Q: 3. Show that A is positive if and only if A B B for some B.

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Q: ,- ). Show that there a 3,4

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Q: Prove that if a and b are both positive, and a2 < b2 then a < b          (Use Indirect Proof)

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Q: have the following properties:

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Q: Prove the following identity ASAP

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Q: Prove: ДАВС — ДCDA %23

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Q: let 19, b) = 1, them prove that there exists x20 Such that ijzo ax_by = 1

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Q: Use contrapositive to prove that if x, y are positive real numbers, then Vx + y + vã + Vỹ.

A: By using contrapositive we have to prove that if x, y are positive real numbers, then x+y≠x+y.

Q: If A+B+C=90  then  prove that tanAtanB+tanBtanC+tanCtanA=1

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Q: Let α, β, γ ∈ Z. Prove: If  α2 + β2 = γ2. then α or β is even.

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Q: Prove that if ACB, then A-B=0.

A: This question can be solved using the concept of set theory.

Q: R is commutative if and only if R[x] is Commutative. True or False

A: The given statement is true. If Rx is cummutative.So, R⊂RxRx is cummutative.R is also…

Q: Let P (x) be the statement "x = x²." If the domain consists of the integers, give True/False…

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Q: Verify the following Identities: 2. 1. (asinx + bcosx) +acos x-bsinx) =a*+b° 2.

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Q: Use contrapositive to prove that if x, y are positive real numbers, then Vx + y # Vã + Vỹ.

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Q: Prove that 1.9 = 2.

A: To prove: 1.9=2

Q: Prove that √2+√5 is irritational

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Q: Prove the following statement using the axioms and lemmas For all nonzero real numbers w, x and y,…

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.