Search & Filtering
There were 100 students in the library who responded to how they completed their research paper. • 18 students only used the periodicals. • 29 students used the web and books. • 15 students used books, the web, and periodicals. • 40 students used books and periodicals. • 20 used the web and periodicals. • 60 students used books. • 7 students did not use the web, nor books, nor the periodicals. a) Represent this information with a Venn diagram. (8 marks) b) How many students only used the web in their research? (2 marks) c) How many students used books or periodicals?
draw a binary search tree by inserting the values 50, 76, 21, 4, 32, 64, 15, 52, 14, 100, 83, 2, 3 and 70.
A class contains 10 students with 6 boys and 4 girls. Find the number of ways: i. A 4 member committee can be selected from the students. ii. A 4 member committee with 2 boys and 2 girls can be selected from the students. iii. A 4 member committee at least 3 boys can be selected from the students.
(i) Use Karnaugh map to minimize the following SOP expression and also implement the simplified expression.
Y = A’BC + A’B’C’ + ABC’ + AB’C’
Q3:
List the 16 different relations on the set {0,1}.
Note: No partial credit would be admissible in this question.
Q2:
Let R be the parent relation on the set of all people (see Example 21 in section 9.1
of the book). When is an ordered pair in the relation R^3?
SUGGESTED TEXT:
· Keneth H. Rosen. Discrete Mathematics and its Applications. 7th edition.
Q1:
Determine whether the relation R on the set of all people is reflexive, symmetric,
antisymmetric, and/or transitive, where (a,b) ∈ R if and only if
a) a is taller than b.
b) a and b were born on the same day.
c) a has the same first name as b.
d) a and b have a common grandparent.
given that the function f(x) = 4x + 1 , find a formula for f-1(x)
Define a binary relation P from R to R as follows: for all real numbers x and y, (x,y)∈P⇔x=y^2. Is P a function? Explain.
We have 5 distinct jobs to be finished in the first 22 days of June but no two of the jobs will be finished on consecutive days. In how many ways can we plan the finishing days for these 5 distinct jobs? Write your answer: the number of ways this can be done is
