Is the argument valid? Use rules of inference and laws of logic
to prove or disprove (no Truth tables)
1. If John has talent and works very hard, then he will get a
job. If he gets a job, then he’ll be happy. Hence if John is not
happy, then he either not worked very hard or does not have
talent.
2.For spring break Marie will travel to Cancun or Miami. If she
goes to Cancun, she will not visit...
Identify (using the most appropriate of lists, rules, or
notation) the elements of each of the following sample spaces:
1) Weight of a randomly selected crawfish
2) A cubic die and a octahedron (8 sided) die being rolled
3) Human IQ
4) Days till next hurricane hits Baton Rouge
5) A die being rolled until an odd number is obtained thrice in
a row
Determine which inference procedures we studied in Chapters
20-23 are appropriate for an- alyzing the following situations, and
justify your answer (for example, ‘I’d use a two sample confidence
interval for comparison of means because...’). You don’t need to
carry out any of the procedures.
(a) How seriously do people view speeding in comparison with
other annoying behaviors? A large random sample of adults was asked
to rate a number of behaviors on a scale of 1 (no problem at...
Prove the following using the method suggested:
(a) Prove the following either by direct proof or by
contraposition:
Let a ∈ Z, if a ≡ 3 (mod 5) and b ≡ 2 (mod 5), then ab ≡ 1 (mod
5).
(b) Prove the following by contradiction:
Suppose a, b ∈ Z. If a² + b²
is odd, then (2|a) ⊕ (2|b), where ⊕ is the exclusive
disjuntion,
i.e. p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q).
(d)...
Calculate all the questions given using appropriate
formulas.(a) You bought a car for RM 30,000 and will borrow RM 30,000 from
the bank for 4 years. The interest charge is 7% per annum. Using
simple interest calculation:How much interest do you have to pay to the bank?
What is the total payment for your car?
(b) You bought a house for RM 300,000 and will borrow RM 300,000
from the bank for 4 years. The interest charge is...
Using only the rules of SD, derive the following rules of
SD+:
a) Disjunctive Syllogism (one case) :
P v Q
~P
b) Commutation: (wedge only) :
P v Q <--> Q v P
c) Implication :
P ⊃ Q <--> Q ⊃ ~P
d) Double Negation
P <--> ~~P
e) DeMorgan
(~(P & Q) <--> ~P v ~Q only)
Use SL sentences rather than metavariables in your derivations.
Each direction of replacement rules must be shown (that is, you...
Match the following events of an action potential to the
most appropriate description. Answers will only be used
once.
Question 1 options:
1234
Resets electrical conditions of the neuron following an action
potential
1234
An exceptionally strong stimulus can trigger a subsequent action
potential
1234
Voltage-gated sodium channels are open, and the neuron cannot
respond to another stimulus
1234
The intracellular side of the neuronal membrane becomes less
negative due to an influx of sodium ions
1.
Relative refractory period...
Prove the following theorem. Using the ruler function axiom. List
all axioms and definitions used.
Let P and Q be two points, then the line segment AB=BA (AB and
BA have lines over them to show line segments)
Prove the following using the triangle inequality:
Given a convex quadrilateral, prove that the point determined by
the intersection of the diagonals is the minimum distance point for
the quadrilateral - that is, the point from which the sum of the
distances of the vertices is minimal.