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**Discrete Mathematical Structures Questions **

**Discuss the following with a suitable example: Integral Domains.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Discuss the following with a suitable example: Euclidian Domain**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Discuss the following with a suitable example: Fields**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Discuss the following with a suitable example: Integral Domain**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Discuss the following with a suitable example: Ideals**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let E = xy = xyz + ryz, prove that z + E ?E**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let E = xy = xyz + ryz, prove that x+ E ?E**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let E = xy = xyz + ryz, prove that xz + E = E**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let G be a finite graph with n> 1 vertices. Prove that then the following statements are equivalent. G is connected and has n-1 edges.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let G be a finite graph with n> 1 vertices. Prove that then the following statements are equivalent. G is cycle-free and has n-1 edges.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let G be a finite graph with n> 1 vertices. Prove that then the following statements are equivalent. G is a tree**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Prove that a graph G with n vertices, n-1 edges and no circuits is connected.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Suppose J and K are ideals in a ring R. Prove hat J n K is an ideal in R.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let S = N x N. Let * be the operation on S defined by (a, b)=(a+ a, b + b) Show that S is a semigroup.Show that f is a homomorphism. Define f: (S,*)?(Z,+) by f(a, ) =a-b.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**How many different words can be formed with the letters of the word BHARAT ? In how may of these B and H are never together. How many of these words begin with B and end with T?**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**The students in a hostel were asked whether they had a dictionary (D) or a thesaurus (T) in their rooms. The results showed that 650 students had a dictionary, 150 did not have a dictionary. 175 had thesaurus and 50 neither a dictionary nor a thesaurus. Find the number k of students who: Live in the Hostel. Have both dictionary and a thesaurus.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Consider the character set given by {a, b, c}. How many 4 lett4er word are possible where any character can e repeated any number of times.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**What that {0} is an ideal in any ring R.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Show that (a-1)-1 = a for any element in a Group G.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**What is monoid?**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**What is a bijective function?**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Let X ={a, b} and Y={1, 2, 3}. Find the number n of functions for Y into X.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**A sample of 80 car owners revealed that 24 owned station wagons and 62 owned cars which are not station wagons. Find the number k of people who owned both a station wagon and some other car.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**What is the difference between walk and paths in graphs?**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**A 2-chromatic graph must be a tree. Is the statement TRUE or FALSE, justify.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Find the number of distinct permutations that can be formed from all the letters of the word UNUSUAL.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**How many different reflexive, symmetric elations are there on a set with three elements?**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**What is a congruence relation on semigroup? Explain.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**Solve the following recurrence relation:s(k) 10 s (k-1) +9 s (k-2) =0.where s(0) = 3 and s(1) = 11.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures

**What is a Quotient ring? Explain with example.**

(class:
BE/BTech - Computer Science
)
Discrete Mathematical Structures