What is Pascal’s triangle? Explain. 

A and B are mutually exclusive events such that P(A) = 1/3 and P(B) = 1/4 .

Find . What is the probability of , and why? 

 How many different professional committees of 8 people can be formed, each containing at least 4 Managers, at least 2 Public Servants and 2 IT Professionals from a list of 8 Managers, 6 Public Servants and 8 IT Professionals? 

 What is a relation? Explain with an example. What are the different types of relations? Explain with an
example for each. 

How many words can be formed using the letters of “EXCEPTIONAL”, using each letter at most
once? 
i) If each letter must be used,

ii) If some or all the letters may be omitted.

Explain the symmetric difference of sets with the help of real-life examples. 

 What is a tautology? If P and Q are statements, show whether the statement

 is a tautology or not.

Construct logic circuites for the following Boolean expressions:

i) (x+yz) + (yz)' + (z'y)

ii) ( x'y) (xz') (y'z) + xyz

 Explain use of the inclusion-exclusion principle with an example.

 Explain proof by contradiction with the help of an example. 

Show whether  is rational or irrational. 

Write down a suitable mathematical statement that the following symbolic properties can represent.
i) 

ii) 

Draw Venn diagram to represent the following. 

i) 

ii) 

iii) 

Give geometric representation for the following. 

i) 

ii) 

Make the truth table for the following.

Here is the transcription of the text and mathematical formulas from the image:
i) 

ii) 

iii) 

What is a proper subset ? Write the number of proper subsets of the Set 

{2, 3, 4, 5, 6, 7, 8, 9}

 What is Set? Explain use of Sets in problem solving.

 [cite: 18]

Make the truth table for the following. (3 Marks) [cite: 9, 12]
i)  [cite: 14]
ii)  [cite: 15]
iii)  [cite: 16]

 What is a proper subset? Write the number of proper subsets of the Set {2, 3, 4, 5, 6, 7, 8, 9} (2 Marks) [cite: 7, 8, 11]