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Discrete Mathematics
b) What is the value of x after each of these statements is encountered in a computer program, if x =3 before the statement is reached?
i) if x +2=5 then x := 3*x +5
ii) if (x +1=4) OR (2x +2=3) then x := x +1
iii) if (2x +3=5) AND (3x +4=13) then x := x^2 +x+7
iv) if (x +1=4) XOR (x +2=5) then x := x +1
v) if x<2 then x := 4*x^3
i) if x +2=5 then x := 3*x +5
ii) if (x +1=4) OR (2x +2=3) then x := x +1
iii) if (2x +3=5) AND (3x +4=13) then x := x^2 +x+7
iv) if (x +1=4) XOR (x +2=5) then x := x +1
v) if x<2 then x := 4*x^3
Discrete Mathematics
a) Let p, q, and r be the propositions
p : You study hard.
q : You are on merit
r : You do not get degree from Iqra University.
Express each of these propositions as an English sentence.
i) ¬q ↔ r ii) q →¬ r iii) p∨q ∨¬r iv) (p →¬r)∨(q →¬r) v) (p∧q)∨(¬q ∧¬r)
p : You study hard.
q : You are on merit
r : You do not get degree from Iqra University.
Express each of these propositions as an English sentence.
i) ¬q ↔ r ii) q →¬ r iii) p∨q ∨¬r iv) (p →¬r)∨(q →¬r) v) (p∧q)∨(¬q ∧¬r)
Discrete Mathematics
How many numbers are divisible by 2, 5, 9, and 13 between 100 and 100,000? How to implement this question in discrete math ?
Discrete Mathematics
Prove that log2 3 is irrational.
Discrete Mathematics
There are two webcams, X and Y that can automatically switch On or Off at any given time to record
a live video streaming session. To ensure the smooth recording session, the live feed input system
is programmed with certain criteria. The conditions set are; if webcam X and webcam Y are switch
on, the input system can enable the recording input and the live session will start. If either webcam
X or webcam Y is switched on, the input system cannot enable the recording and the live session
will stop. In all other conditions, the input system will enable the recording and the live session
streaming will commence.
c. Translate the pseudocodes in part (a.) and (b.) into propositional logic statements.
a live video streaming session. To ensure the smooth recording session, the live feed input system
is programmed with certain criteria. The conditions set are; if webcam X and webcam Y are switch
on, the input system can enable the recording input and the live session will start. If either webcam
X or webcam Y is switched on, the input system cannot enable the recording and the live session
will stop. In all other conditions, the input system will enable the recording and the live session
streaming will commence.
c. Translate the pseudocodes in part (a.) and (b.) into propositional logic statements.
Discrete Mathematics
(i) Give a formal definition of a graph G and its complement G.
(ii) Draw the graph with degree sequence 4, 4, 4, 4, 4, 4 and show that it is unique.
(iii) Suppose a graph G has (0, 1) adjacency matrix A(G) = A. Write down the adjacency
matrix of G in terms of the all-one matrix J and identity matrix I.
(ii) Draw the graph with degree sequence 4, 4, 4, 4, 4, 4 and show that it is unique.
(iii) Suppose a graph G has (0, 1) adjacency matrix A(G) = A. Write down the adjacency
matrix of G in terms of the all-one matrix J and identity matrix I.
Discrete Mathematics
Show graphically that which of the following is one to one function
(1)f(x)=ln(x)
(2)g(x)=e^x
(3) h(x)=x³
(1)f(x)=ln(x)
(2)g(x)=e^x
(3) h(x)=x³
Discrete Mathematics
Model two contextualized problems using binary trees both quantitatively and qualitatively.
Discrete Mathematics
Suppose S is a set containing 5 elements, and that ⪯ is a total ordering of S. Draw the Hasse diagram for ⪯ (no need to label the vertices in your diagram).
Discrete Mathematics
From a set of numbers 1-15, how many numbers should be picked to form pair of numbers that adds up to 16? Illustrate the solution.
