②、④（把符合要求的命题序号都填上）．
分析：通过举出反例：a=1，b=-1，可以说明①是假命题；根据角π4的正切值，结合必要条件的含义，可得②是真命题；根据两个数的积不等于0的含义，可得“xy≠0”是“x≠0或y≠0”的充分不必要条件，得到③是假命题；根据充分必要条件的含义，通过举出反例可得到④是真命题．由此可得正确答案．解答：解：对于①，“a-b＞0”不是“a2-b2＞0”的充分条件，可举出反例：a=1，b=-1，满足“a-b＞0”，但是“a2-b2＞0”不成立，故①是假命题；对于②，若“α=π4”成立，则tanα=tanπ4=1，结论“tanα=1”成立，故“tanα=1”是“α=π4”的必要条件，②是真命题；对于③“xy≠0”说明x≠0且y≠0，所以“xy≠0”是“x≠0或y≠0”的充分非必要条件，故③是假命题；对于④“两个三角形相似”是“两个三角形面积相等”既充分也不必要条件，比如两个相似三角形的相似比为2：1时，它们的面积不相等，说明充分性不成立，再如△ABC是边长为2的等边三角形，△DEF是两条直角边分别为2和3的直角三角形，则△ABC和△DEF的面积都等于3，但它们显然是不相似的，故④是真命题．根据以上所述，可得真命题序号为②④故答案为：②④点评：本题根据几个命题真假的判断，着重考查了充分条件、必要条件、充要条件和既不充分与不必要条件的理解与判断，属于中档题．
请选择年级高一高二高三请输入相应的习题集名称(选填)：
科目：高中数学
9、下列四个命题：①A∩B=A；②A∪B=B；③A∩（CuB）=φ；④A∪B=U．其中与命题A⊆B等价的共有（　　）A、1个B、2个C、3个D、4个
科目：高中数学
平面α与β平行，且a?α，下列四个命题中①a与β内的所有直线平行&&&&&&&&&&②a与β内的无数条直线平行③a与β内的任意一条直线都不垂直&&④a与β无公共点其中真命题的个数是（　　）A．1B．2C．3D．4
科目：高中数学
有下列四个命题：①a与b的夹角为锐角的充要条件是a•b＞0．②?x，y∈R，sin（x-y）=sinx-siny；③?a∈（0，1）∪（1，+∞），函数f（x）=a1-2x+1都恒过定点(12，2)；④方程x2+y2+Dx+Ey+F=0表示圆的充要条件是D2+E2-4F≥0；其中正确命题的序号是②③．（将正确命题的序号都填上）
科目：高中数学
若a，b为不重合直线，α，β为不重合平面，给出下列四个命题：①a?αb∥a⇒b∥α；②a⊥αb⊥α⇒b∥a；③α∩β=ab∥α⇒b∥a；④a⊥αa⊥b⇒b∥α；其中真命题的个数为（　　）A．0个B．1个C．2个D．3个
科目：高中数学
已知下列四个命题：①a是正数；②b是负数；③a+b是负数；④ab是非正数．选择其中两个作为题设，一个作为结论，写出一个逆否命题是真命题的复合命题．
吴老师30日19点直播线段的垂直平分线的性质
余老师30日20点直播unit5第二课时 Section AFrom Wikipedia, the free encyclopedia
Drosophila sex-chromosomes
Ginkgo biloba
The XY sex-determination system is the
found in , most other , some insects (), and some plants (). In this system, the
of an individual is determined by a pair of sex chromosomes (gonosomes). Females have two of the same kind of sex
(XX), and are called the . Males have two distinct sex chromosomes (XY), and are called the .
This system is in contrast with the
found in , some insects, many , and other animals, in which the heterogametic sex is female.
system is found in some reptiles.
have a set of
coding for
present on . In humans, most mammals, and some other species[], two of the , called the
and , code for sex. In these species, one or more
present on their
that determine maleness. In this process, an
act to determine the sex of offspring, often due to genes located on the Y chromosome that code for maleness. Offspring have two sex chromosomes: an offspring with two X chromosomes will develop female characteristics, and an offspring with an X and a Y chromosome will develop male characteristics.
Human male XY chromosomes after
In humans, a single gene () present on the Y chromosome acts as a signal to set the developmental pathway towards maleness. Presence of this gene starts off the process of . This and other factors result in the . The cells in females, with two X chromosomes, undergo , in which one of the two X chromosomes is inactivated. The inactivated X chromosome remains within a cell as a .
Humans, as well as some other organisms, can have a chromosomal arrangement that is contrary to
for example,
or XY females (see ). Additionally, an abnormal number of sex chromosomes () may be present, such as , in which a single X chromosome is present, and , in which two X chromosomes and a Y chromosome are present,
and . Other less common chromosomal arrangements include: , , and .
XY system in mammals: Sex is determined by presence of Y. "Female" due to the absence of the Y. In the 1930s,
determined that the presence of
was required for
development in the male rabbit.
sex-determining gene on the Y chromosome in the
(placental mammals and marsupials). Non-human mammals use several genes on the Y-chromosome. Not all male-specific genes are located on the Y-chromosome. Other species (including most
species) use the presence of two X chromosomes to determine femaleness. One X chromosome gives putative maleness. The presence of Y-chromosome genes is required for normal male development.
Main article:
Birds and many insects have a similar system of sex determination (), in which it is the females that are heterogametic (ZW), while males are homogametic (ZZ).
Many insects of the order
instead have a system (the ), where the males are
individuals (which just one chromosome of each type), while the females are
(with chromosomes appearing in pairs). Some other insects have the , where just one chromosome type appears in pairs for the female but alone in the males, while all other chromosomes appear in pairs in both sexes.
PBB Protein SRY image
For a long time, biologists believed that the female form was the default template for the mammalian fetuses of both sexes. After the discovery of the , many scientists shifted to the theory that the genetic mechanism that determines a fetus to develop into a male form was initiated by the SRY gene, which was thought to be responsible for the production of
and its overall effects on body and brain development. This perspective still shared the class that in order to produce two sexes, nature has developed a default female pathway and an active pathway by which male genes would initiate the process of determining a male sex, as something that is developed in addition to and based on the default female form. This view is no longer considered accurate by most scientists who study the genetics of sex. In an interview for the Rediscovering Biology website, researcher Eric Vilain described how the paradigm changed since the discovery of the SRY gene:
For a long time we thought that SRY would activate a cascade of male genes. It turns out that the sex determination pathway is probably more complicated and SRY may in fact inhibit some anti-male genes.
The idea is instead of having a simplistic mechanism by which you have pro-male genes going all the way to make a male, in fact there is a solid balance between pro-male genes and anti-male genes and if there is a little too much of anti-male genes, there may be a female born and if there is a little too much of pro-male genes then there will be a male born.
We [are] entering this new era in molecular biology of sex determination where it's a more subtle dosage of genes, some pro-males, some pro-females, some anti-males, some anti-females that all interplay with each other rather than a simple linear pathway of genes going one after the other, which makes it very fascinating but very complicated to study.
In mammals, including humans, the SRY gene is responsible with triggering the development of non-differentiated
into testes, rather than . However, there are cases in which testes can develop in the absence of an SRY gene (see ). In these cases, the
gene, involved in the development of testes, can induce their development without the aid of SRY. In the absence of SRY and SOX9, no testes can develop and the path is clear for the development of ovaries. Even so, the absence of the SRY gene or the silencing of the SOX9 gene are not enough to trigger sexual differentiation of a fetus in the female direction. A recent finding indicates that ovary development and maintenance is an active process, regulated by the expression of a "pro-female" gene, . In an interview for the TimesOnline edition, study co-author Robin Lovell-Badge explained the significance of the discovery:
We take it for granted that we maintain the sex we are born with, including whether we have testes or ovaries. But this work shows that the activity of a single gene, FOXL2, is all that prevents adult ovary cells turning into cells found in testes.
Looking into the genetic determinants of human sex can have wide-ranging consequences. Scientists have been studying different sex determination systems in
and animal models to attempt an understanding of how the genetics of sexual differentiation can influence biological processes like reproduction, ageing and disease.
In humans and many other species of animals, the
determines the
of the child. In the XY sex-determination system, the female-provided
contributes an X
and the male-provided
contributes either an X chromosome or a Y chromosome, resulting in female (XX) or male (XY) offspring, respectively.
Hormone levels in the male parent affect the sex ratio of sperm in humans. Maternal influences also impact which sperm are more likely to achieve .
Human ova, like those of other mammals, are covered with a thick translucent layer called the , which the sperm must penetrate to fertilize the egg. Once viewed simply as an impediment to , recent research indicates the zona pellucida may instead function as a sophisticated biological security system that chemically controls the entry of the sperm into the egg and protects the fertilized egg from additional sperm.
Recent research indicates that human ova may produce a chemical which appears to attract sperm and influence their swimming motion. However, not all sperm are some appear to remain uninfluenced and some actually move away from the egg.
Maternal influences may also be possible that affect sex determination in such a way as to produce
equally weighted between one male and one female.
The time at which insemination occurs during the oestrus cycle has been found to affect the sex ratio of the offspring of humans, cattle, hamsters, and other mammals. Hormonal and pH conditions within the female reproductive tract vary with time, and this affects the sex ratio of the sperm that reach the egg.
Sex-specific mortality of embryos also occurs.
Since ancient times, people have believed that the sex of an infant is determined by how much heat a man's sperm had during insemination. Aristotle wrote that:
...the semen of the male differs from the corresponding secretion of the female in that it contains a principle within itself of such a kind as to set up movements also in the embryo and to concoct thoroughly the ultimate nourishment, whereas the secretion of the female contains material alone. If, then, the male element prevails it draws the female element into itself, but if it is prevailed over it changes into the opposite or is destroyed.
Aristotle claimed that the male principle was the driver behind sex determination, such that if the male principle was insufficiently expressed during reproduction, the
would develop as a female. In contrast, modern genetics has developed a view on sex determination in which no one single factor is responsible a number of pro-male, anti-male and pro-female genes being responsible, though the largest factor is whether the male's gamete carries an X or Y chromosome.
are credited with discovering, in 1905, the chromosomal XY sex- the fact that males have XY sex
and females have XX sex chromosomes.[]
The first clues to the existence of a factor that determines the development of testis in mammals came from experiments carried out by , who castrated embryonic rabbits in utero and noticed that they all developed as female.[]
In 1959, C. E. Ford and his team, in the wake of Jost's experiments, discovered that the Y chromosome was needed for a fetus to develop as male when they examined patients with , who grew up as phenotypic females, and found them to be X0 ( for X and no Y). At the same time, Jacob & Strong described a case of a patient with Klienfelter's syndrome (XXY), which implicated the presence of a Y chromosome in development of maleness.
All these observations lead to a consensus that a dominant gene that determines testis development () must exist on the human Y chromosome. The search for this
(TDF) led a team of scientists in 1990 to discover a region of the Y chromosome that is necessary for the male sex determination, which was named
(Sex-determining Region of the Y chromosome).
for information on variations in human sexual forms
Fauci, Anthony S.; Braunwald, E Kasper, Dennis L.; Hauser, Stephen L.; Longo, Dan L.; Jameson, J. L Loscalzo, Joseph (2008). Harrison's Principles of Internal Medicine (17th ed.). McGraw-Hill Medical. pp. .  .
(PDF). Utrecht University - Department of Biology. Ultrecht, Netherlands 2014.
Jost, A.; Price, D.; Edwards, R. G. (1970). "Hormonal Factors in the Sex Differentiation of the Mammalian Foetus [and Discussion]". Philosophical Transactions of the Royal Society B: Biological Sciences 259 (828): 119–31. :.  .
Wallis MC, Waters PD, Graves JA; W Graves (June 2008). "Sex determination in mammals - Before and after the evolution of SRY". Cell. Mol. Life Sci. 65 (20): 3182–95. :.  .
Rediscovering Biology, Unit 11 - Biology of Sex and Gender, Expert interview transcripts,
Uhlenhaut, N. H et al. (2009). "Somatic Sex Reprogramming of Adult Ovaries to Testes by FOXL2 Ablation". Cell 139 (6): 1130–42. :.  .
, Hannah Devlin, The Times, December 11, 2009.
Tower, J Arbeitman, Michelle (2009). . Journal of Biology 8 (4): 38. :.  .  .
Krackow, S. (1995). . Biological Reviews 70 (2): 225–241. :.
Suzanne Wymelenberg, Science and Babies, National Academy Press, 1990, page 17
Richard E. Jones and Kristin H. Lopez, Human Reproductive Biology, Third Edition, Elsevier, 2006, page 238
De Generatione Animalium, 766B 15-17.
Jost A., Recherches sur la differenciation sexuelle de l’embryon de lapin, Archives d'anatomie microscopique et de morphologie experimentale, 36: 271 – 315, 1947.
FORD, CE; JONES, KW; POLANI, PE; DE ALMEIDA, JC; BRIGGS, JH (Apr 4, 1959). "A sex-chromosome anomaly in a case of gonadal dysgenesis (Turner's syndrome)". Lancet 1 (7075): 711–3. :.  .
JACOBS, PA; STRONG, JA (Jan 31, 1959). "A case of human intersexuality having a possible XXY sex-determining mechanism.". Nature 183 (4657): 302–3. :.  .
Schoenwolf, Gary C. (2009). "Development of the Urogenital system". Larsen's human embryology (4th ed.). Philadelphia: Churchill Livingstone/Elsevier. pp. 307–9.  .
Sinclair, Andrew H.; et al. (19 July 1990). "A gene from the human sex-determining region encodes a protein with homology to a conserved DNA-binding motif". Nature 346 (6281): 240–244. :.  .
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Understanding the
Inverse Sine Function
The Function y = sin-1x = arcsin x and its Graph:
Since y = sin -1x is the inverse of the function y = sin x, the function y = sin-1x if and only if sin y = x. But, since y = sin x is not one-to-one, its domain must be restricted in order that y = sin-1x is a function.
To get the graph of y = sin-1x, start with a graph of y = sin x.
Restrict the domain of the function to a one-to-one
region - typically is used (highlighted in red at right) for sin-1x. This leaves the range of the restricted function unchanged as [-1, 1].
Reflect this graph across the line y = x to get the
graph of y = sin-1x (y = arcsin x), the black curve at right.
Notice that y = sin-1x has domain [-1, 1] and range . It is strictly increasing on its entire domain.
So, when you ask your calculator to graph y = sin-1x, you get the graph shown at right. (The viewing window is [-2, 2] x [-2, 2].)
Evaluating y = sin-1x:
Example 1: Evaluate sin-1(1/2)
Most people are more familiar (and more comfortable) with the trigonometric functions than their inverses. Therefore, the first step in evaluating this expression is to say that if y = sin-1(1/2), then sin y = 1/2. This simple trigonometric function has an infinite number of solutions:
Five of these solutions are indicated by vertical lines on the graph of y = sin x below.
So, is the value of sin-1 (1/2) given by the expressions above? No! It is vitally important to keep in mind that the inverse sine function is a single-valued, one-to-one function. Only one of the infinite number of solutions given above is the result we want. Which one? Remember that the range of sin-1x is , which is indicated in blue in the figure above. It is really important to know the domain and range of the inverse trigonometric functions! (Why is this blue interval marked on the x-axis if it represents the range of sin-1x? Because the range of the inverse function equals the domain of the principal function.) The only solution of y = sin x that falls within the required range is
(the solid red line in the figure above). Therefore,
Example 2: What is
A unit-circle diagram is shown at right.
Notice that candidates for the solution include:
However, only one of these values is in the range of sin-1x (), so:
The Derivative
of y = sin-1x:
The derivative of y = sin-1 x is: (Click
for a derivation.)
The graphs of y = sin-1 x and its derivative is shown at right. The domain of y' is (-1. 1). Since y = sin-1 x is always increasing, y' & 0 for all x in its domain.
Integrals Involving the Inverse Sine Function
Since , . This means that the arcsine function arises in discussions involving integrals (and areas) of &relatively normal looking& algebraic functions. For instance:
This is the shaded area shown in the TI-89 screen shot at right. (The window is [-0.5, 1.1] x [0, 3].)
last update January 16, 2009 by}