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Construct the truth tables for the following compound propositions.
1. (๐ โง ๐) โ (๐ โจ ๐)
2. (๐ โ ๐) โจ (โผ ๐ โ ๐)
3. [(๐ โ ๐) โง (๐ โ ๐)] โ (๐ โ (๐ โง ๐))
4. โผ (๐ โง ๐) โ (๐ โจโผ ๐)
5. (๐ โ ๐) โจ ๐
The result of the nationwide aptitude test in mathematics are normally distributed with a mean of 70 and standard deviation of 5. Find the raw score such that 60% of the cases are below it and case above it.ย ย
let i=<x,2> and=<x,3> be ideal in z[x] .prove that IJ=<x,6>
Suppose that A = {1,3,5}, B = {1,5}, C = {3,7}, and D = {1,3}. Determine which of these sets are subsets of๏ปฟ which other of these sets.๏ปฟ
4. Using the sample space for rolling two dice, construct a probability distribution for the random variable X representing the sum of the numbers that appear.
find the mean of the probability distribution of the random variable X if P(X)=โ , for X= 1,2,2....,10
Joe is in charge of purchasing office supplies and his budget is $175.00. Paper is $21.99 a box, toner cartridges are $52.90 each, and folders are $0.99 each. All office supplies are 20% off. If Joe needs to buy 3 boxes of paper and 2 toner cartridges, how many folders can he buy?
Consider the linear equation 2a + 3b = 4
Is (a; b) = (1; 1
2
) a solution to the equation? Motivate your answer.
10 Look up the concept of a homogeneous linear system.
Which of the following linear systems is homogeneous. [just give the answer I) or II) or III) : no motivation
is required.]
I) 3x + 14y = 0 & 2x โ 3y = 7
II) 7x + 2y = 10 & 11x โ 0y = 7
III) 4x โ 23y = 0 & 7x โ 3y = 0
11.) You have a linear homogeneous system in three variables. Give a solution that this system must have.
T
If RโS, then TโR โ TโS and RโT โ SโT
