Discrete Mathematics Answers

Expand the following Boolean functions into their canonical form:
i. f(X,Y,Z)=XY+YZ+ X Z+ X Y
ii. f(X,Y,Z)=XY+ X Y + X YZ

If we have 100 people (80 male and 20 female) and we need to choose a committee.
The committee must contain exactly 2 females, then how many different 5 person committees are possible?

In a certain village of 1000 houses, 750 have a car, 800 have a refrigerator, 850 have a telephone and 950 have a radio. What is the least number of houses that have all four?

Consider the sample space S = {copper, sodium, nitrogen, potassium, uranium, oxygen, zinc}, and the events A={copper, sodium, zinc}, B={uranium, nitrogen, potassium}, C={oxygen}.
List the elements of the sets corresponding the following events:
i) A ∪ C
ii) (A ∩ B') ∪ C'
iii) (A' ∪ B') ∩ (A' ∩ C)

How many bit strings of length five either begin or end with a 1?

How many maximum number of bit strings of length five are possible?

a) Which of the following functions are 1-1 and which are onto? Justify your answer.
i) f : R!R0 given by f (x) = x2 where R0 is the set fx 2 Rjx 0g.
ii) f : R!R given by f (x) = x2+x+1.

Sophia asked the students in her class to name their favorite sport. She made this list to display the results, 1/3 of the students names basketball, 1/8 of the students named soccer, 5/12 of the students named football. The rest of the students in te class named baseball. What fraction of the students in the class named baseball as their favorite sport?

Roxanne sits and writes roxyroxyroxyroxyroxy... If she continues, determine the 2134th letter she will write down

1. The cost of a piece of cloth is Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 les
s, the cost would remain unchanged. How long is the piece.
2. In a group of 50 people; 35 speak Hindi, 25 speak both English and Hindi and all people speak at least one of the two languages. How many people speak only English and not Hindi? How many people speak English?
3.Which is a better investment 14% stock at 95 or 15% stock at 105?
4.There are two types of fertilizers
1Fand2F.1F consists of 10% nitrogen and 6% phosphoric acid and 2 F consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that he atleast needs 14 kg. of nitrogen and 14 kg of phosphoric acid for the crop. If 1F costs Rs. 6 per kg. and 2F costs Rs. 5 per kg., determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost.