Find dual of Boolean Expression for the output ( Y) of the followinglogic circuit

Show whether √7 is rational or irrationl

Explain use of inclusion-exclusion principle with example

(b) Make logic circuit for the following Boolean expressions: (4) i) (xyz) + (xyz)' + (xz'y) ii) ( x'yz) (xyz') (xy'z)

What is counterexample? Explain its use with the help of an example.

Give geometric representation for followings: (3) i) {5, -3) x ( -2, -2) ii) {-1, 3) x ( -2, 3)

Explain whether the function f(x) = x + 1 is one-one or not.