12(a)
(b)

13(a)
(b)

14(a)

(b)

15(a)

(b)

16(a)

(b)

17(a)
(b)

0800MAT203122001

pat

न
Show that ((p > q) ^ (क > 7)) > ‏م)‎ > 7) isa tautology.
Let 2, ۹,۲ be the statements given as
p: Arjun studies. ஏ: He plays cricket. 7: He passes Data Structures.
Let 91, 22, 23 denote the premises
‏:رم‎ If Arjun studies, then he will pass Data Structures.
72: If he doesn't play cricket, then he will study.
p3: He failed Data Structures.

Determine whether the argument (2) Ap2 Ap3) > q is valid.

Module 2
State Binomial theorem. Find the coefficient of xyz? in (2x — y — z)*
Determine the number of positive integers n such that 1 100 and n is
not divisible by 2,3 or 5.
Prove that if 7 distinct numbers are selected from (1,2,3, ...,11}, then sum of
two among them is 12.
An um contains 15 balls, 8 of which are red and 7 are black. In how many
ways can 5 balls be chosen so that (i)all the five are red (ii)all the five are
black (iii) 2 are red and 3 are black (iv)3 are red and 2 are black.

Module 3
If f,g and hare functions on integers, f(n) = n?,g(n) =n + 1,
h(n) = n - 1, then find (1) f°g°h (ii) g°f°h (111) h°f°g
If A = {a,b,c} and P(A) be its power set. The relation < be the subset
relation defined on the power set. Draw the Hasse diagram of (P(A), S).
Let R be a relation on 7 by xRy if 4|(x —y). Then find all equivalence
classes.
Find the complement of each element in 042.

Module 4
Solve the recurrence relation a,4; = 2a, +1,n = 0, dg = 0.

Solve the recurrence relation 6,.+2 = ‏ربہہہ‎ tan ,7 = 0, 60 = 0, 61 = 1

Page 2 of 3

(6)
(8)

(6)
(8)

(6)

(8)

(6)

(8)

(6)

(8)

(6)
(8)