Math Answers

1.    Show that are logically equivalent. P ↔ Q and (P ∧ Q) V ( ¬P ∧ ¬Q)

 Your answer sheets showing your name and solution.

1. Given the following:

·        g: "You can graduate."

·        m: "You owe money to the college."

·        r: "You have completed the requirements of your major."

·        b: "You have an overdue book."

Translate "You can graduate only if you have completed the requirements of your major, you do not owe money to the college, and you do not have an overdue book." into a propositional logic.

2. Show that  are logically equivalent.

3. Show, by the use of the truth table (truth matrix), that the  is a contradiction.

Given

[1 1 -1]

A=[2 2 3]

[4 0 0]

[1 1 -1]

b=[2 2 3]

[4 0 0]

1.Find –A^-1+ 3B^T

2.Find B^-1+ ( A^T+A^-1)

Solve for the determinant in the equation below

2 −2 1

2 2 1

4 1 3

Solve for the determinant in the equation below.

4 −3 2

1 2 −2

2 -1 −4

  Find the product of 10101₂ and 101₂.  

If the mean and the standard deviation of a continuous random variable that is normally distributed are 19 and 5 respectively, what is the interval that contains 95% of the distribution? *

Solve the following equation using inverse method

[1 3 0] [x] [4]

[0 0.5 1] [y]=[1]

[0.5 0 1] [z] [3]

A cylindrical container has one end opened and the other end closed. It has a circular base of radius r cm. Given that the total surface area of the container is 200π cm2.

(a) Show that the volume of the container is V = 100πr - πr^3/2 cm3

(b) Find the maximum value of V.

The ages of participants in a drama workshop are normally distributed with mean 18.5 years and standard deviation 2.5 years. What is the probability that the age of a random participant is (a) more than 20 years, (b) between 16 and 18 years?