C1B001 Pages: 2

(a) There are no restrictions.

(b) There must be 5 men and 5 women.

(c) There should be an even number of men.
(d) There should be at least 8 men.

OR
14. (1) Define Pigeonhole principle. Consider any group of 6 people, where any two
people are either friends or enemies, then show that there are either 3 mutual friends
or 3 mutual enemies.

(ii) Find the coefficient of x y z in the expansion of (x+y+z)

MODULE IV
15. Solve + = 3r(2)
OR
16. Solve -4 +3 = -200 , 000 ; given that =3000, =3300.
MODULE V

17. Let G= (४, E) be an undirected graph or multi graph with no isolated vertices. Show
that G has an Euler circuit if and only if G is connected and every vertex in G has
even degree.

OR
18. Use Fleury’s algorithm to find an Euler circuit for the following graph.

MODULE VI

19. Show that the following argument is valid: “If today is Monday, I have a test in
Physics or Mathematics. If my Physics professor is sick, I will not have a test in

Physics. Today is Monday and my Physics professor is sick. Therefore I have a test in
Mathematics”

OR
20. Use rules of inference to show that $xM(x) follows logically from the premises

(x) H(x)®M(x) and $xH(x).

ید بد بد ‎मे‏

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