"If today is a holiday then I will not go to school". Write inverse and for this sentence. contrapositive 

Show, using the pigeonhole principle, that in any group of 30 people, 5 people can always be found who were born on the same day of the week.

Find dual of Boolean Expression for the output (P) of the following logic circuit.

Write the following statements in symbolic form:

(i) Mahesh is hardworking student therefore he is a good performer.

(ii) Either exercise regularly or be ready for poor health.

What is a function? Explain how to find inverse of a function with the help of an example.

Prove +C "C, + "C,n

Explain addition theorem in probability with an example.

Three Sets A, B and Care: A= {1, 3,5,7,9,12,13, 15,17}, B= {1,2, 3,7,8,9, 10,17} and C {1,2,7, 8, 10, 11, 12,13,173. Find A B C; A~BUC; ABCand(A~C)

How many wa

ys are there to distribute 29 district items into 5 distinct boxes with:At least two empty box.

i) At least two empty box.

ii) No empty box.

iii) Explain principle of multiplication with an example

Let fand g be the two functions such that  Define fof, fog, gof and gog.

Explain whether the function f(x) = x²+2 is one-one or not.

Find how many 3 digit numbers are even?

A and B are mutually exclusive events such that P(A) = 1/4 and P(B)= 1/2 and P (AU B) = 1/6. What is the probability of P(A ∩ B)?

A committee consisting of 5 male and2 female workers is to be constituted from 8 male and 9 female workers. In how many distinct ways can this be done?

What is a tautology? If P and Q are statements, show whether the statement  tautology or not.

Prove that 

How many words can be formed using letter of "DETERMINATION" using each letter at most once?

i) If each letter must be used,

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

What is a relation? Is every relation a function? Explain critically. Also, explain equivalence relation with the help of example.

Draw logic circuit for the following Boolean expressions:

i)   

ii)  

iii)  

Explain applications of inclusion-exclusion principle with example.