This document contains a midterm exam for a discrete structures course. The exam has 4 questions worth a total of 24 marks. Question 1 contains 6 multiple choice questions worth 1 mark each. Question 2 defines functions such as injective, surjective and bijective functions. Question 3 finds the 11th term of an arithmetic sequence and simplifies a logical statement using laws of logic. Question 4 uses a truth table to show a statement is a tautology and shows a argument form is valid using rules of inference.

1. KAIMS INTERNATIONAL INSTITUTE MULTAN
(MID TERM)
Program: BSCS Subject: Discrete Structure
Teacher Name: Engr. Zain Ul Abdeen Date: …./5/2017
Total Marks: 24 Time Allowed: 60 Minutes
Note:Attempt All questions,Each questioncontainsequal marks:
Q.No.1: (𝟏 ∗ 𝟔 = 𝟔 𝑴𝒂𝒓𝒌𝒔)
1. The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________.
a) {1, 2, 6, 1}
b) {1, 2, 5, 6}
c) {1, 2, 1, 2}
d) {1, 5, 6, 3}
2. For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {an} is ____________.
a) 3n+1
– 2
b) 3n
– 2
c) (-3)n
+ 4
d) n2
– 2
3. A statement is referred to as a
a) Proposition
b) Conclusion
c) Order
d) None of these
4. An argument is --------------------- if the conclusion is true when all the premises true
a) Valid
b) Invalid
c) False
d) None of these
5. The row in the truth table of an argument where all premises are true is called
a) Valid Row
b) Invalid Row
c) Critical Row
d) None
6. The negation of “Today is Friday” is
a) Today is Saturday
b) Today is not Friday
c) Today is Sunday
d) None

2. Q.No.2: Define the followingfunctionswith the helpof example (𝟔 𝑴𝒂𝒓𝒌𝒔)
a) Injective Function
b) Surjective Function
c) Bijective Function
Q.No.3: (𝟔 𝑴𝒂𝒓𝒌𝒔)
a) Find the 11th term of the arithmeticsequence whose 6th term is 5 and 8th term is 11.
b) Usinglaw of logic,simplifythe statement form
p  [~(~p  q)]
Q.No.4: (𝟔 𝑴𝒂𝒓𝒌𝒔)
a) Use truth table to show that (p  q) (~p(p ~q)) is a tautology.
b) Show that the followingargumentform is valid:
pq
p
 q