# Define zero-one matrix. Explain the types of function.

Zero-one matrix:

• A matrix with entries that either 0 or 1 is called a zero-one matrix.
• Zero-one matrix are often used to represent discrete structures.
• The boolean arthematic is based on the boolean operations ∨ and ∧, which operate on pains of bits defined by

b1 ∧ b2 = $$\left\{\begin{matrix}1 \enspace if \enspace b_1 = b_2 = 1\\ 0 \enspace otherwise\end{matrix}\right.$$

b1 ∨ b2 = $$\left\{\begin{matrix}1 \enspace if \enspace b_1 = 1 \enspace b_2 = 1\\ 0 \enspace otherwise\end{matrix}\right.$$

Types of Function:

There are three types of function:

1. One to one function(Injective):

A function is called one to one if for all elements a and b in A, if f(a) = f(b),then it must be the case that a = b. It never maps distinct elements of its domain to the same element of its co-domain.

2. Onto function(Surjective):

A function is called an onto function if each element in the co-domain has at least one pre – image in the domain.

2. Bijective function:

A function from A to B is one-to-one correspondence orbijective, if f is both injective(one-to-one) and surjective(onto).