Questions

Unit-I

1. In a survey of 5000 people. It was found that 3000 play tennis, 250 play football and 200 play both tennis and football. Find how many people play either tennis or football or both.

2. How many integers between 1 to 1000 are divisible by 2, 3, 5 or7?

3. Show that by principle of mathematical induction n^4-4n^2 is divisible by 3 for all n>=0 

4.  Write short notes on
 i) Tautology and Contradiction
 ii) Universal of Existential.

5. Write short notes

Countability of Rational Numbers Using Cantor Diagonalization Argument 

Unit-II

1. Let A is the set of factors of positive integer  m and relation is divisibility on A i.e R={(x,y)| x, y belongs to A, x divides y} for  m=45.show that POSET(A,<=) is a lattice. Draw Hasse diagram and give join and meet for the lattice. 

2. Find the transitive closure of the relation R on A={1,2,3,4} defined by R={(1,2),(1,3),(1,4),(2,1),(2,3),(3,4),(3,2),(4,2),(4,3)} 

3. Show that if 7 colors are used to paint 50 bicycles at least 8 bicycles will be of the same colour. 

4. Let R={(1,4),(2,1),(2,5),(2,4),(4,3),(5,3),(3,2)} use warshalls algorithm to find the matrix of transitive closure 

Let R={(1,4),(2,1),(2,5),(2,4),(4,3),(5,3),(3,2)} use warshalls algorithm to find the matrix of transitive closure