Answer:
Let P(x) = x is in the correct place
Let Q(x) = x is in the excellent place
R(x) denotes the tool
Explanation:
a) Something is not in the correct place.
P(x) is that x is in the correct place so negation of ¬P(x) will represent x is not in the correct place. ∃x is an existential quantifier used to represent "for some" and depicts something in the given statement. This statement can be translated into logical expression as follows:
∃x¬P(x)
b) All tools are in the correct place and are in excellent condition.
R(x) represents the tool, P(x) represents x is in correct place and Q(x) shows x is in excellent place. ∀ is used to show that "all" tools and ∧ is used here because tools are in correct place AND are in excellent condition so it depicts both P(x) and Q(x). This statement can be translated into logical expression as follows:
∀ x ( R(x) → (P(x) ∧ Q(x))
c) Everything is in the correct place and in excellent condition.
Here P(x) represents correct place and Q(x) represents excellent condition ∀ represent all and here everything. ∧ means that both the P(x) and Q(x) exist. This statement can be translated into logical expression as follows:
∀ x (P(x) ∧ Q(x)
def dx(fn, x, delta=0.001):
return (fn(x+delta) - fn(x))/delta
def solve(fn, value, x=0.5, maxtries=1000, maxerr=0.00001):
for tries in xrange(maxtries):
err = fn(x) - value
if abs(err) < maxerr:
return x
slope = dx(fn, x)
x -= err/slope
raise ValueError('no solution found')
Answer:
The TAB key
Explanation:
Sam would use the TAB key, located on the left side of the keyboard, to move around his document to add stops and format its information properly.
Pressing the TAB key will introduce a tab code in his document, which is like moving ahead by a certain number of spaces (5,6, 10 spaces for example, depending on the configuration of the document), but without using spaces, using a tab which is a much better option to position, align things up.
