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i)                  Which type of relation is shown in below expression

R1 = { (a,b) | a = b } 


25. Solve recurrence relation an+3=3an+2+4an+1-12an for n20 with a0-0,al--11,a2--15


Is (p>q)>[(p>q)>q] a tautology? Why or why not?


Prove or disprove ¬(¬p -> q) =¬(p Ú q) is correct.


Show that (p → r) ∨ (q → r) and (p ∧ q) → r are logically equivalent. 


a)     (p ↔ q) ⊕ (¬p ↔¬r)

b)     (p → q) ∧ (¬p → r)



You have been working as a mathematical analyst for the Everest Statistics Bureau Pvt. Ltd. operating in Kathmandu Nepal. The Bureau helps the Government of Nepal by providing statistics in developing Public Policy Planning, Collecting and Analyzing Socio-Demographic Data and developing methodologies for reliable data collection and implementation of various researches. Research such as technological aspects and developmental work of the country. With the use of data recorded from various sources, they are using mathematics to determine the fastest routes and time for travelling different corners of the city to free the general public from traffic congestion. With the help of a minimum weighted spanning tree, they are trying to use the least amount of pipelines to connect all the terminals of the locality.


{(0,-5),(1,-4),(2,-3),(3,-2),(4,-1),(5,0)}

Is this a relation


Let A be {a, b, c}. Let the relation R be {(c, b), (a, a), (b, c)}. Which of the following statements about R is true?
a. R is not reflexive, is not symmetric, and is not transitive.

b. R is reflexive, is symmetric, and is not transitive.

c. R is reflexive, is not symmetric, and is not transitive.

d. R is not reflexive, is symmetric, and is not transitive.

What are the differences between relations and functions?


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