Discrete Mathematics Answers

One hundred students were asked whether they had taken course in any of the three areas, CSE,

ME and EE. The results were.

45 had taken CSE, 38 had taken ME, 21 had taken EE, 18 had taken CSE and ME, 9 had

taken CSE and EE, 4 had taken ME and EE and 23 had taken no courses in any of the three

areas.

(i) Draw a Venn diagram that will show the results of the survey?

(ii) Determine the number K of students who had taken courses in exactly?

b) One of the areas b) Two of the areas c) Nor in CSE, nor in ME but in EE

Theorem 2:-

An (m,n) encoding ∅ corrects

K or fewer errors if and only if the minimum distance between encoded words is atleast 2K+1

Proof:-

Suppose that ∅ corrects K or fewer errors x is an encoded word of distance 1≤j≤k from the encoded word y.

Theorem 1:-

An (m,n) encoding ∅ detects K or fewer errors if the minimal distance between encoded words is atleast K+1

Proof:-

Assume that ∅ detects all sets of K of fewer errors

With example in mathematical foundations of computer science

What and Define The Hamming Metric with example in mathematical foundations of computer science

Show that the relation R = ∅ on a nonempty set S is symmetric and transitive but not reflexive.

Answer the following items. Show your complete answer on a separate sheet of paper.

Prove that the following sentences are tautologies.

1. p →p

2. p → (p V q)

3. [p Λ (p → q)] → q

4. p V ~p

5. q → (p V ~p)

6. ~p → (p →q)

7. (p Λ q) → p

8. (p → q) → [(p V r) → (q V r)]

9. ~q → ~(q Λ r)

Let R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}

R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}

is a relation on set A={1,2,3,4}

A={1,2,3,4}

Suppose a Rn b

means that there is a path of length n from a

to b

Which of the elements are R3?

How many pairs of dance partners can be selected from a group of 12 women

and 20 men?

4. Let A and B be sets. Prove the commutative laws from Table 1 by showing that

a) A ∪ B = B ∪ A.

b) A ∩ B = B ∩ A.