Discrete Mathematics Assignment - II

Discrete Mathematics	AY 2018-19
Assignment –II	Date of submission:  11/08/2018

Q1. Let R be a symmetric relation. Show that Rⁿ is symmetric for all positive integers n.

Q2. Let R be the relation on the set of all urls such that xRy iff the web page at x is the same as the web page at y. show that R is an equivalence relation.

Q3. Let R be reflexive relation on set A. Show that R Í  R²

Q4. Determine whether each of these functions is a bijection from R to R

i.                   f(x)= 2x+1

ii.                 f(x)= x²+1

iii.              f(x)= x³

Discrete Mathematics Assignment -I

Discrete Mathematics	AY 2018-19
Assignment –I	Date of submission:  11/08/2018

Q1. Show that for any two sets A & B

                                    P(A) È P(B) Í  P(AÈB)

Q2. Prove that

                                    (AÇ B) X (CÇ D) = (AXC) Ç (BXD)

Q3. Let A and B be subsets of universal set U.

Show that A ÍB if and only if B’Í A’

Q4. State the rules of inference.

Q5. Using rules of inference, show that conclusion follows from hypothesis.

            Hypothesis:

            P: if there is a gas in car then I will go to store.

            Q: if I go to the store, then I will get soda.

            R: there is gas in car.

            Conclusion:    

                        I will get soda.

Q6. Using rules of inference, show that conclusion follows from hypothesis.

            Hypothesis:

            P: Everyone in class has graphing calculator.

            Q: Everyone who has graphing calculator, understands trigonometric function.

Conclusion:

            Avyaan, who is in class, understands trigonometric function. 

Set Identities

Sets are one of the basic building blocks for the types of objects considered in discrete mathematics. to manipulate set equations, we needs set identities. I have listed few of them in the following document. 

Deletion of a node from Binary search tree

You can find my presentation on deletion of node from Binary search tree here...

Discrete Mathematics Questions

Discrete Mathematics Questions

Detailed Draft_BE_Syllabus_2012

You can refer to draft of BE syllabus here...

Draft_BE_Syllabus_2012

You can refer to draft of BE syllabus here...