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

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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.

- Hamro CSIT

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.

- Hamro CSIT

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).

- Hamro CSIT

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