21MA1305 – MATHEMATICAL FOUNDATION FOR MACHINE LEARNING
UNIT – I LOGIC AND PROOFS
ASSIGNMENT - I
1. Show that the expression P  Q  P  R  Q  R  R is a tautology by using
truth table.[AP][CO1]
2. Without using truth table, show that ~ P  ~ Q  R  Q  R  P  R  R
.[AP][CO1]
3. Show that the premises R   Q , R  S , S   Q , P  Q , P are inconsistent.
[AP][CO1]
4. Find the PCNF of P  R   P  Q . Also find its PDNF, without using truth
table[AP][CO1]
5. Show that if x and y are integers and both x y and x  y are even, then both x and
y are even. [U][CO1]
6. For the following set of premises, explain which rules of inferences are used to obtain
conclusion from the premises. ‘Somebody in this class enjoys whale watching. Every
person who enjoys whale watching cares about ocean pollution. Therefore, there is
person in this class who cares about ocean pollution”. [AP][CO1]
21MA1305 – MATHEMATICAL FOUNDATION FOR MACHINE LEARNING
UNIT – II COMBINATORICS
ASSIGNMENT – II
1. Use mathematical induction to show that
1
1

1
2

1
3
 ......... 
1
n
 n ,n2
[AP][CO2].
2. Using mathematical induction prove that if n is a positive integer, then 133 divides
11n1 12 2 n 1 . [AP][CO2].
3. Solve the recurrence relation a n   3 a n  1  3 a n  2  a n  3  1 with a0  5 , a1   9 and
a2  15 [AP][CO2].
4. Find the solution to the recurrence relation a n  6 a n 1 11 a n  2  6 a n  3 with the initial
conditions a0  2 , a1  5 and a2  15 [AP][CO2].
5. Use
the
method
of
generating
function,
solve
the
S n  3 S n  1  4 S n  2  0 ; n  2 given S 0  3 and S1   2 [AP][CO2].
recurrence
6. Find the number of integers between 1 and 500 that are not divisible by any of the
integers 2 , 3 and 5 [AP][CO2].