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Let P(x, y) be the statement "x takes y ", where the domain for x consists of all people and y consists of train to work.

a Everyone takes train to work.

b There is someone who took train to work.

c There is someone who took at least one train to work.

d Everyone takes at least one train to work.

e Someone takes at least one train to work.


  1. Let P(x, y) be the statement "pupil x has taken class y", where the domain for x consists of pupils and y consists of Discrete Mathematics. Express each of the quantification in English sentences.

a.∀x∀y P(x, y)

b∀x∃y P(x, y)

c∃x∃y P(x, y)

d∃x∀y P(x, y)



Find the percentile rank of the 18 using the following data: 15, 13, 6, 5, 12, 22, 50, 18

Two ships A and B sail simultaneously from the same place. vessel A on course 300at 15 knots and B on course N 45°E at 10 knots. After 1 hour and 30 min, How far is vessel B from the starting point?




A proton moves through a uniform magnetic field of magnitude 2.0 μT at a speed of 5.00x10^6 m/s.


(a) What is the magnitude of the maximum magnetic force it can experience?

(b) If the proton is replaced by an electron, will it experience the same maximum force?


Clas calld Author is desiged tomodel book author.Contan:3private intance varable:name(String),email(String),and gender(char of either 'm' or 'f');An__init__() toinitalize the nme,email,gendr with given value Getters/Setters: getName(),getEmail(),setEmail(),and getGender()(There areno seter for nameandgender, asthese atribute canotbe changd.)A__str__() metodthat return prntable string oftht objct with folowing formt:

"Author[name=?,email=?,gender=?]"

e.g., "Author[name=Tan Ah Teck,email=ahTeck@somewhere.com,gender=m]". Write the Author clas.Writetest driver code totest all public functon e.g.,

ahTeck=Author("Tan Ah Teck", "ahteck@nowhere.com", 'm')#Test the  constructor

print(ahTeck) # Test __str__()

ahTeck.setEmail("paulTan@nowhere.com") #Test setter

print("Name is: ", ahTeck.getName())#Test getter

print("Email is: ", ahTeck.getEmail())#Test getter

print("Gender is: ",ahTeck.getGender())#Test getter.


For argon the numerical value of a is 1.337 and the numerical


value of b is 0.0320.



Use the van der Waals equation to calculate the pressure of a


sample of argon at-90.0 °C with a molar volume of 2.59 L/mol.


Round your answer to the correct number of significant digits.

The amount of lemonade in a 2 litre bottle is normally distributed with a mean of 2.1 liters and a standard deviation of 0.07 liters.The portion of bottles that actually contain more than 2 liters is ?

Random samples with size 5 are drawn from the population containing the values 26, 32, 41, 50, 58, and 63. Determine the standard error of the sample means.


Random samples with size 5 are drawn from the population containing the values 26, 32, 41, 50, 58, and 63. Find the mean of the mean of the sample means. 


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