Download I A not gate of the type p = not q is called an inverter, for it simply

I
A not gate of the type p = not q is called an inverter, for it simply inverts the input signal, wheter or not it
be current or voltage. It is the simplest logic gate at all (àthere are not logic gates like that). When the
input is high, for instance, the output is low (that is, not high). If compared to the other gates, it is the
exception: it takes only one input (ànot more than one) producing one output based solely on that input.
The word “not” suggests a contradiction: and that’s exactly what a not gate does: it denies. We can create
an inverter using a single transistor, say an npn, a high-gain one, and make it behave like an inverter. Its
industrial application is not negligible. There must be a voltage regulator in the circuit in order for the
voltage spread not to exceed 5V. As for the transistor we have from left to right the emissor, followed by
the base, followed by the collector. The emissor is connected to ground. The base cannot get to ground
like that, but needs being connected through a 100-ohm resistor to a wire we use as a switch for the circuit.
When this last wire is connected to the ground we have an input of 0 (meaning 0 conditional, no
implication). We have then a 100-ohm resistor that connects the high rear to the collector of the transistor
and another 100-ohm resistor connecting it to ground through the LED, which is now ON, the switch being
not on an ON position. That gives us our not circuit: if we switch to 1 moving the wire from 0 to 5V, then
the output in the LED zone is going to give us a value of 0, so that it won’t be any longer on an ON position,
but on an OFF one. In other words when the input is 0, the transistor is in cutoff, which means it behaves
like a very large resistor. This forces the current to flow through the 100-ohm resistor to the collector of the
transistor. From here, since the emissor is off (it is not connected, or not in a non-ground position), it flows
through the other resistor and, via the LED, to ground: in this case the LED lights. When we switch from 0 to
5V we can see the LED goes off (it does not light). Here the transistor in saturation. This means that the
current flows freely between the collector and the emissor, so it acts like a short circuit (no, or a very low
electrical impedance is encountered) and does not flow through the resistor leading to ground through the
LED, but directly to ground from the emissor. Because of this the LED does not light.
II
Today’s Genetics says a chromosome is a singled piece of coiled DNA containing many genes. To
oversimplify things we can say that particular genes, such as eye color or tooth size, are located at a same
certain point of a chromosome from both the parents: they are called homologous chromosomes. If we call
one point b (that stands for blue eyes) and the other B (that stands for brown eyes), then we can write our
genotype as Bb. Each of the way this eye-color gene is expressed is an allele, so that the b and the B in Bb
are two different alleles, or versions of the same gene. When I have two different versions of this, one from
my mom and the other from my dad, I’m called a heterozygous genotype then the genotype is the exact
version of the allele I have. If I were a lowercase b / lowercase b (bb), or a upper case B / upper case B (bb),
then I would have two identical alleles, both of my parents giving me the same version of the gene. In this
case I am a homozygous genotype, or I am a homozygote for this trait. Assuming the idea that Brown are
dominant traits and blue are recessive traits. This means that if I were to inherit the Bb genotype, because
the B allele is dominant, then all you are going to see for the person with this genotype is brown eyes. In
this way, a genotype is the actual version of the gene you have and a phenotype is what is expressed, or
what you see. So many different genotypes are all coded for the same phenotype: Bb, bB, BB à brown
eyes; bb à blue eyes. Considering, for example, my parents as being both heterozygous, we can build a
mono-hybrid cross –that is, a grid known as “punnett square”, which is useful for each kind of crosses
between two reproducing organisms:
B
b
B
BB
Bb
b
bB
bb
III
Compound inequalities are inequalities that have more than one set of constraints. Let’s consider our
problem as being negative 5 less than or equal to x minus 4, which is also less than or equal to 13. In
symbols: -5≤x-4≤13. So we have two sets of constraints on the set of xs that satisfy both these inequalities: x
minus 4 has to be greater or equal to -5 and less than or equal to 13. Consequently we can rewrite this
inequality as -5≤x-4 and x-4≤13. We can solve them separately, and then we have to remember to think
about the solution set, because the “and” reminds us the set has to be things that satisfy both inequalities.
If we solve them separately we get x≥-1 and x≤17. Compounding we get -1≤x≤17, so that [-1,17] is the
interval notation for the entire inequality. Now, let’s say 4x-1 needs to be greater than or equal to 7 or 9x
over 2 needs to be less than 3. In symbols, 4x-1≥7 ⋁ 4x-1< 3. So now when we are saying “or”, an x that
would satisfy these inequalities are xs that satisfy either of them. Here this is much more lenient than the
“and” problem: we have to satisfy one of the two. So let’s figure out the solution set for both: it means we
have to figure out essentially their union. We realize it needs to be x≥2 or x< 2/3. If we had an “and” instead
of an “or”, there would have been no numbers that satisfy this inequality, because numbers can’t be both
greater than 2 and less than 2/3. So the only way that there is any solution set here is because it is “or”. You
can satisfy one of the two inequalities.
IV
[Brief introduction in order to outline the target] We have fed chocolate to a bunch of female chickens and
we got 31 female chicks and 17 male chicks. To get the sex ratio we need to calculate the probability of
getting each possible number of males, from 0 to 48, under the null hypothesis that 0.5 are male.
[Body of the text containing graphs, data analysis, calculations, manipulations, word-problems and the like
AS A PART OF THE TEXT]To this extent we do a histogram showing the probability as a function of the
number of males.
It clearly turns out that the probability of getting exactly 17 males out of 48 total chickens is about 0.015.
What we want to know, however, is the probability of getting 17 or fewer males. If we were going to accept
17 males as evidence that the sex ratio was biased, we would also have accepted 16, or 15, or 14,… males
as evidence for a biased sex ratio. We therefore need to add together the probabilities of all these
outcomes. The probability of getting 17 or fewer males out of 48, under the null hypothesis, is 0.030. That
means that if we had an infinite number of chickens, half males and half females, and we took a bunch of
random samples of 48 chickens, 3.0% of the samples would have 17 or fewer males.
[Conclusion] We have realized that we need a different Probability number when adding statements. This
number 0.030, is actually the P value we are interested in. It is defined as the probability of getting the
observed result, or a more extreme result, if the null hypothesis is true. So "P=0.030" is a shorthand way of
saying "The probability of getting 17 or fewer male chickens out of 48 total chickens, if the null hypothesis
is true that 50% of chickens are male, is 0.030.“.
EXERCISES
•
Deconstruct the 4 texts into atomic propositions and recompound them changing and/or
readapting the logical connectives so that either the meaning stays the same or it gets altered.
•
Label both atomic and molecular propositions.
•
Build up appropriate and/or truth tables using 1 for true and 0 for false statements.
•
Write the corresponding if clauses 1,2,3.
•
Text building: use whatever source consistent with your scientific course and write down a
coherent text using atomic and molecular propositions appropriately connected to one another.
Include any graph or table as a part of the body of the text.