Discrete Mathematics
Max Marks: 30
Note: The Question paper is divided into three sections A, B, and C. Write Answer as per the given instruction.
Section-A (Very Short Answer Type Questions)
Note: Answer all questions. As per the nature of the question you delimit your answer in one word, one sentence or maximum up to 30 words. Each question carries 1 mark. 6×1=06
Q.1 What is Number System ?
Q.2 What is Positional Number System?
Q.3 Which one is the Value of ? (A58)16 = (?)10
Q.4 Which is the value of ? (100101)2 = (?)10
Q.5 Covert (10001)2 = (?)10
Q.6 Write the binary digits used to record the word COMPUTER in BCD?
Section-B (Short Answer Questions)
Note: Answer any four questions. Each answer should not exceed 100 words. Each question carries 3 marks. 4×3=12
Q.1 Prove that :-
- A U (B U C) =(A U B) C
Q.2 Prove that ?
- A U (B C) = (A U B) (A U C)
Q.3 Prove that
- (A U B)’ = A’ B’
Q.4 Find the converse, inverse and contra positive of the following conditional “only Mohan teaches good will he get good results”
Q.5 Let R be a relation from a set X ={a,d,c}to set Y = {x,y,z}given by the Set R ={(a,x), (a,y), (b,z) }.Then find the domain and range of the relation R
Section ‘C’ (Long Answer Questions)
Note: Answer any two questions. You have to delimit your each answer maximum up to 400 words. Each question carries 06 marks.
Q1.Write the ASCII-7 coding for the word “GIRL” in binary and hexadecimal notations. How many bytes required to store this word using this coding?
Q2. Find the converse, Inverse and contra-positive of the following:
- If today is rainy day, then tomorrow is Sunday.
- If A is rectangle, then P is a square.
- If Ram is good , then he is honest.
Q3. Let R3 be an equivalence relation on the set Z of integers such that “(a, b) ∈R3 if 3 | (a-b)”. Then find the partitions induced by R3 in Z.
Q4. Prove that the dual of a lattice is again a lattice.
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