Question and Answers Forum
Set TheoryQuestion and Answers: Page 1
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Question and Answers Forum |
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Set TheoryQuestion and Answers: Page 1 |
| Find Card{(A,B,C)∈P(E)^3 / AUBUC=E} |
| Find ∫_0 ^∞ (((−1)^(E(x)) )/(E(−x)))dx |
| 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 |
| 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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| 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? |
| Let A={x ∈ R∣x^2 <4}and B={y ∈ Q∣y>−3}find A∩B |
| Q)Choose at least some members frome the set A={14,15,...,20,22,23,...,28} so that whith confidence includes three consecutive members? |
| Find f(x)=∫^( x) _( 0) (dt/(t+e^(f(t)) )) |
| 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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| 1×3×5×7×9×...×2005 = ... (mod 1000) |
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| Prove that ∫^( (π/2)) _( 0) ((ln(1+αsint))/(sint))dt= (π^2 /8)−(1/2)(arccosα)^2 |
| prove that lim_(x→0) (((Σ_(k=1) ^n (1−(1/(2k)))^x )/n))^(1/( x )) = (1/4)(C_(2n) ^n )^(1/n) |
| Prove that for any set A containing n elements, ∣P(A)∣=2^n . |
| 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 ) |
| Prove that ∀n∈IN ∫^( 1) _( 0) t sin^(2n) (lnt)dt= (1/(1−e^(−2π) )) ∫^( π) _( 0) e^(−2t) sin^(2n) (t)dt |
| f_(n ) the general sentence is seqiencee fibonacci. prove that : f_(2n−1) =f_n ^2 +f_(n−1) ^2 |
| Show that in fibonacci sequence f_(3n) =f_n ^3 +f_(n+1) ^3 −f_(n−1) ^3 |
| if f_n =f_(n−1) +f_(n−2) ; f_1 =f_2 =1 then prove that 5∣f_(5n) |