Discrete Mathematics "UExam" Semester-ll, 2022

Discrete Mathematics "UExam" Semester-ll, 2022

 UNIVERSITY OF EDUCATION LAHORE

"UExam" Semester-ll, 2022

BS Information Technology, Session 2021-2025

Course Code: MATH2113
Subject: Discrete Mathematics
Time Allowed: 100 Minutes.

Max. Marks: 56

Section II (Short Answer)

Q.2- Write short answers of the following

• 1- Let A=b {a,b,c} consider the relation g= {(a,b),(b,c),(c,c)} is g one-to-one ? is g onto?why?
• 2-. Let A = (1, 2, 3,4). define a binary relation on a set A which is reflexive, symmetric and transitive?
• 3-. Let p and q be the propositions the election is decided and the votes have been counted respectively . Express the compound propositions as an English sentence.
• ~q v (~p ^q)
• 4-. The answer sheets of discrete mathematics are to be labelled  with three character ,a letter, a digit and a letter. What is the largest number of answer sheets that can be labelled differently?
• 5-  What rule of inference is used in this argument?
• If i go swimming, then I will stay in the sun too long. If I stay in the sun too long. then I will sunburn. Therefore if i go swimming  then i will sunburn.
• 6-List all the steps used to search for 11 in the sequence 2, 3, 7, 8, 10, 11, 13, 1, 17 using binary search.
• 7- List the three differences between Graphs and Trees.
• 8- How many rows appear in a truth tabble for the following compound propositions?
• (p~r) V (~s~-t)V (~u-v)

Section lII (Essay Type)

Answer the following Questions

Question No 3# Find n and r if nPr =3024 and nCr- 126, where P represents permutation and C represents combination.

Question 4: Prove that v 7 is irrational by giving a proof by contradiction,
Question No 5: Does the graph in following diagram have a Hamiltonian path ? if so, find such three
Paths. If it  does not. give an argument to show why no such path exists.

  A               B

  D               C

         E

Question 6 : Answer these questions about the tree given below
 (a) which vertices are siblings of 0?
(b) Which vertices are ancestors of m?
(e) what is the height of q?
(a) what s the depth of f?