Math Answers

Prove that the set Z of all integers with binary operation * defined by a*b=a+b+1

for all a, b belonging to G is an Abelian group.

Suppose U and V are subspace of R^n with U intersection V={0}. if {u1,.....uk} is a basis for U and {v1,.....vL} is a basis for V, prove that {u1.....uk,v1.......vL} is a basis for u+v.

1. How many 4 digits numbers can we create from 3,4,5,6,7,0,9 if;
2. We need all numbers to be even numbers        [2]
3. We need all of them to be odd numbers        [2]
4. We need all of them to be divisible by 5        [3]
5. In how many different ways can we choose a committee that is comprised of two men and one woman from a group of 5 men and 4 women if;
6. We need a chosen committee member is selected only once (i.e. if a person occupies only one position in the committee)                [2]
7. We need to choose a chairperson, a treasurer and secretary [3]

In how many ways can we arrange the letters of the word EXCELLENT to form different 9 letter words, with or without meaning   

A sample 10 pieces was examined out of a large consignment which has 5% defective pieces .Give the probability of 1 defective in the sample of 10.

Show that the following logical equivalences hold for the

Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).

a. ∼P ≡ P ↓ P

b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)

c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)

H d. Write P → Q using Peirce arrows only.

e. Write P ↔ Q using Peirce arrows only.

solve the differential equation by the method of variation of parameters d²y/dx²+9y=sec3x

For a sample of volume 61, average values were found x = 5.574 , y =14.492 , 2 x = 34.361, 2 y = 213.639, xy = 83.148 . Find sample linear correlation coefficient and check its significance on level 0.05.

For a sample of volume 61, average values were found x = 5.574 , y =14.492 , 2 x = 34.361, 2 y =213.639, xy = 83.148 . Find sample linear correlation coefficient and check its significance on level 0.05.

Find the variance of a discrete random variable X - the number of occurrences of event A in four independent tests, if the probability of occurrence of event A in each test is 0.1. Write in the form of a table the law of distribution of the random variable X

There are 10 stalls for animals in an exhibition. Three animals; lion, pussycat

and horse are to be exhibited. Animals of each kind are not less than 10 in

number. What is the possible number of ways of arranging the exhibition?