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A student can choose a computer project from one of three lists. The three lists


contain 23, 15 and 19 possible projects, respectively. How many possible


projects are there to choose from?

Consider the recurrence relation an= 3 an1 + 3 an-2 when ao = 1 and a1= 2 then a3= ..: O 56


Produce truth tables for given Boolean expressions

A’B’C + AB’C + ABC + ABC’


2. A survey on subjects being taken by 250 college students in Candon City revealed the following information.



Subject Number of students taking the subject

Mathematics 145

Filipino 90

English 88

Math and Filipino 25

Filipino and English 38

Math and English 59

Math, Filipino and English 15


How many did not take any of the three subjects?

How many took Math as their only subject? English only? Filipino only?

How many were taking Math and Filipino but not English?

How many were taking Filipino and English but not Math?



3Fn − Fn−2 = Fn+2, for n ≥ 3.


what is symbolic form of she did nit received a promotion or she did not received a salary increase

What is symbolic form of it is not true that, the students answered their activity or participated in the class discussion

The ages of 100 persons are tabulated below. Find Q1, Q3, D2, D8, P20 and P60. Above what age


we have the oldest 10% persons?


Age(in years) 10-20 20-30 30-40 40-50 50-60 60-70 70-80


No. of persons 16 20 21 28 10 3 2


Note: the oldest 10% are above P90.


Ans.: P20 = 22, P60=41.071, the oldest 10% persons are of the age 55 and above.

Calculate the quartiles, (i,e., Q1 and Q3,), deciles D3 and D7, Percentiles P10, P23 and P92 for the


following data. Also find the Quartile Range and Quartile Deviation.


Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80


No. of Students 8 7 5 12 28 22 8 10

Translate the following statement into mathematical expression based on the given propositional variables.

“If a country’s leaders are elected based on good leadership traits, then the country will have good governance”.

p : A country’s leaders are elected based on good leadership traits.

q : The country will have a good governance.  

q → pp → qp ⟷ qq ⟷ p


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