Set Theory — Page 1 — Tinkutara Math Forum

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Question 228448

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m_− R (R/m_− ) ⇔

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Question 226170

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Find Card{(A,B,C)∈P(E)^3 / AUBUC=E}

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Find ∫_0 ^∞ (((−1)^(E(x)) )/(E(−x)))dx

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Let f :R_+ →R such as f(xy)=f(x)+f(y) 1) Prove that f is derivable iff f is derivable at x=1. 2) Prove that if so, f(x)=Log_a x) where a is positive value to precise

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given that ϕ,β are the roots of the equation 3x2−x−5=0 from the equation whose roots are 2ϕ−1/β,2β−1/ϕ

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Question 215777

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Question 212974

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Please help 1.1.Let XUY=X for all sets X. Prove that Y=0(empty set). From Singler book "Excercises in set theory". I think this task is totaly wrong and cannot be proved. I would ask someone to provide me valid proof of that. I have sets X and Y such as Y is subset of X. For example. If Y={1} and X={1,2} then XUY=X is correct but that doesn't imply Y is empty. Another example when X=Y since X is any set. I can choose X=Y. Why not? Then YUY=Y is always true, but again, that doesnt imply Y is empty set Proof in book claim that is correct if we suppose Y is not empty and if we choose for instance X is empty set. Then 0UY=0 but this is wrong since 0UY=Y. Therefore, Y must be empty?

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Let A={x ∈ R∣x^2 <4}and B={y ∈ Q∣y>−3}find A∩B

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Q)Choose at least some members frome the set A={14,15,...,20,22,23,...,28} so that whith confidence includes three consecutive members?

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Find f(x)=∫^( x) _( 0) (dt/(t+e^(f(t)) ))

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2^(5m) 5^(2n) 2020^(2020) n+2m

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2 students are passing a test of n questions with the same chance to find each one Show the chance that they both don′t find a same question is ((3/4))^n

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Question 204141

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Question 203737

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a_1 <a_2 <a_3 <...<a_k ((2^(289) +1)/(2^(17) +1)) = 2^a_1 +2^a_2 +...+2^a_k

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1×3×5×7×9×...×2005 = ... (mod 1000)

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Prove that for any set A containing n elements, ∣P(A)∣=2^n .

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Question 199624

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Question 198380

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Prove that ∫^( (π/2)) _( 0) ((ln(1+αsint))/(sint))dt= (π^2 /8)−(1/2)(arccosα)^2

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prove that lim_(x→0) (((Σ_(k=1) ^n (1−(1/(2k)))^x )/n))^(1/( x )) = (1/4)(C_(2n) ^n )^(1/n)

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Prove that (x^3 /(2sin^2 ((1/2)arctan (x/y))))+(y^3 /(2cos^2 ((1/2)arctan (y/x))))=(x+y)(x^2 +y^2 )

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Prove that ∀n∈IN ∫^( 1) _( 0) t sin^(2n) (lnt)dt= (1/(1−e^(−2π) )) ∫^( π) _( 0) e^(−2t) sin^(2n) (t)dt

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f_(n ) the general sentence is seqiencee fibonacci. prove that : f_(2n−1) =f_n ^2 +f_(n−1) ^2

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Show that in fibonacci sequence f_(3n) =f_n ^3 +f_(n+1) ^3 −f_(n−1) ^3

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if f_n =f_(n−1) +f_(n−2) ; f_1 =f_2 =1 then prove that 5∣f_(5n)

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Question 194446

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Use laws of algebra to prove the following (a)[(B−A)u(A−B)]=[(AuB)−(AnB)] (b)A▽(AnB)=A−B

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find a solution; e^x = ln(x)

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a^ 2+2ab+b^ 2

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Question 189672

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1 : Ω = Σ_(n=1) ^∞ (( (− 1 )^( n) H_( n) )/n^( 2) ) = ? 2 : η (−1 )= ?

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Q: G( V , E ) is a graph , such that ∣ V (G )∣ = 20 , Δ ( G )= 8 , δ (G )=3 find the value of , q_( max) − q_( min) = ? q = ∣ E (G )∣

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If , 7^( n) ≡^(10) 7^( 19) then find the 1st digit of the numer , 8^( n+4) .

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Let A={1^(p^2 −p) , 2^(p^2 −p) ,..., (p−1)^(p^2 −p) , p^2 −p+1} where p is any prime number Prove that for any value of p, however we split this set into two disjunctive sets, the arithmetic means of all elements of both sets cannot be equal to each other.

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Question 182129

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Question 181280

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Question 180299

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Evaluate Ω = lim_( n→∞) ( n− Σ_(k=1) ^n cos ( (( (√k))/( n)) ) ) =?

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Question 179918

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Find prime numbers of 3 digits such that equal to sum of 3 diffrent numbers of prime

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ax^2 +bx+c = 0 x = ((−b±(√(b^2 −4ac)))/(2a)) Example: Find the values of x in the equation x^2 +5x+4 = 0 In order to solve for that, let′s first take a look on what are the values of a, b and c 1x^2 + 5x + 4 = 0 a = 1 ; b = 5 ; c = 4 Now, using the quadratic formula x = ((−5±(√(5^2 −4(1)(4))))/(2(1))) = ((−5±(√(25−16)))/2) = ((−5±3)/2)