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Question Number 216751 Answers: 0 Comments: 0

Find Card{(A,B,C)∈P(E)^3 / AUBUC=E}

$${Find}\:\:\:{Card}\left\{\left({A},{B},{C}\right)\in{P}\left({E}\right)^{\mathrm{3}} /\:{AUBUC}={E}\right\} \\ $$

Question Number 216749 Answers: 2 Comments: 0

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

$${Find}\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left(−\mathrm{1}\right)^{{E}\left({x}\right)} }{{E}\left(−{x}\right)}{dx} \\ $$

Question Number 216532 Answers: 2 Comments: 0

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

$${Let}\:{f}\::\mathbb{R}_{+} \rightarrow\mathbb{R}\:{such}\:{as}\:{f}\left({xy}\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$$\left.\mathrm{1}\right)\:{Prove}\:{that}\:\:{f}\:{is}\:{derivable}\:{iff}\:\: \\ $$$${f}\:{is}\:{derivable}\:{at}\:{x}=\mathrm{1}. \\ $$$$\left.\mathrm{2}\left.\right)\:{Prove}\:{that}\:{if}\:{so},\:{f}\left({x}\right)={Log}_{{a}} {x}\right)\: \\ $$$${where}\:{a}\:{is}\:{positive}\:{value}\:{to}\:{precise} \\ $$

Question Number 216355 Answers: 1 Comments: 1

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

$${given}\:{that}\:\varphi,\beta\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\mathrm{3}{x}\mathrm{2}−{x}−\mathrm{5}=\mathrm{0}\:{from}\:{the}\:{equation}\:{whose}\:{roots}\:{are}\:\mathrm{2}\varphi−\mathrm{1}/\beta,\mathrm{2}\beta−\mathrm{1}/\varphi \\ $$

Question Number 215777 Answers: 0 Comments: 0

Question Number 212974 Answers: 1 Comments: 0

Question Number 212332 Answers: 0 Comments: 4

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?

$$ \\ $$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?

Question Number 211643 Answers: 1 Comments: 0

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

$$\mathrm{Let}\:\boldsymbol{{A}}=\left\{\boldsymbol{{x}}\:\in\:\mathbb{R}\mid\boldsymbol{{x}}^{\mathrm{2}} <\mathrm{4}\right\}\mathrm{and} \\ $$$$\boldsymbol{{B}}=\left\{\boldsymbol{{y}}\:\in\:\mathbb{Q}\mid\boldsymbol{{y}}>−\mathrm{3}\right\}\mathrm{find}\:\boldsymbol{{A}}\cap\boldsymbol{{B}} \\ $$

Question Number 209746 Answers: 1 Comments: 1

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

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

Question Number 209246 Answers: 1 Comments: 0

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

$$\mathrm{Find}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{t}+\mathrm{e}^{\mathrm{f}\left(\mathrm{t}\right)} } \\ $$

Question Number 207864 Answers: 1 Comments: 0

$$\:\:\:\:\:\underbrace{\:} \\ $$

Question Number 207372 Answers: 0 Comments: 6

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

$$\mathrm{2}\:{students}\:{are}\:{passing}\: \\ $$$${a}\:{test}\:{of}\:\:{n}\:{questions}\:{with} \\ $$$${the}\:{same}\:{chance}\:{to}\:{find}\:{each}\:{one} \\ $$$${Show}\:\:{the}\:{chance}\:{that}\:{they}\:{both} \\ $$$$\:{don}'{t}\:{find}\:{a}\:{same}\:{question}\:{is}\:\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$

Question Number 204141 Answers: 1 Comments: 0