Assignment : Discrete Mathematics (CS- 503)
Group A
( Predicate logic )
1. Show that t is a valid conclusion from the premises p→q, q→r, r→s, ~s and p˅t.
2. Show that t is a valid conclusion from the premises p→~q, q˅r,~s→p
3. Using predicate logic to write the following sentences in symbolic form
(a) Some boys in the class are taller than all girls
(b) Everyone can fool some person at some time
(c) No one can fool everyone all the time
Group B
( Properties of Integer)
4.
5.
6.
7.
8.
Prove that product of any m consecutive integers is divisible by m.
25x=15(mod 29) , identify the possible values of x.
Use the theory of congruence prove that for n1, 17|(23n+1 + 3.52n+1)
Use the theory of congruence prove that for n1, 27|(25n+1 + 5n+2)
Use the theory of congruence prove that for n1, 25|(2n+4 + 33n+2)
Group C
( POSET and Lattice)
9. For the poset S = ({2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72}, |) find out
(a) the maximal elements,
(b) the minimal elements,
(c) the greatest element,
(d) the least element,
(e) all upper bound of {2, 9},
(f) least upper bound of {2, 9} if it exists,
(g) all lower bounds of {60, 72},
(h) the greatest lower bound of {60, 72} if it exists
10. Draw the Hasse diagram for the poset S = {2, 3, 5, 30, 60, 120, 180, 360} under the relation
division. Hence find maximal, minimal, greatest and least element if exist.
11. Draw the Hasse diagram for divisibility on the set , hence find the GLB and LUB (2,3,12)
{2, 3, 6, 12, 24, 36, 48}