Find how many 4 digit numbers are even? How many 4 digit numbers are composed of odd digits.

Show whether 17 is rational or irrational.

Make logic circuit for the following Boolean expressions:

i) (x′.y + z) + (x+y+z)′ +(x+y+z)

X Y Z

O

ii) ( x'+y).(y′+ z).(y+z′+x′)

X Y Z

O

b) What is dual of a Boolean expression? Find dual of boolean expression of the

output of the following logic circuit:

Ans: If p is a proposition involving ~, ∧ and ∨, the dual of p, denoted by pd, is the proposition

How many different 15 persons committees can be formed each containing at least 2 Accountants and at least 3 Managers from a set of 10 Accountants and 12 Managers.

What are conditional connectives? Explain use of conditional connectives with an example.

No empty box.

~p→(q Ú ~ r) Ù ~p Ù q