# Applied Sciences

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King Abdul Aziz University

Faculty of Computing & Information Technology

Computer Science Department

CPCS-222 (Discrete Structure I)

Assignment 03

Announced Date: July 15, 2020

Due Date: June 18, 2020

Student ID:

Student Name:

***Section: XA

Marks Obtained:

Maximum Marks: 30

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Q.1: (pts 06)

Determine whether f is a function from Z to R

A. f(x) = 1 ⁄ (x 2 − 4)

B. f(x) = ±x

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Q.2: (pts 06)

Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. And

which functions are onto?

A. f (a) = b, f (b) = a, f (c) = c, f (d) = d

B. f (a) = b, f (b) = b, f (c) = d, f (d) = c

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Q.3: (pts 06)

Determine whether each of these functions from R to R is invertible. If so, find its

inverse.

A. f (x) = -3x + 4

B. f (x) = -3×2 + 7

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Q.4: (pts 06)

Find f o g and g o f, where f (x) = x2 + 1 and g(x) = x + 2, are functions from R to R.

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Q.5: (pts 06)

Represent each of these relations on {1, 2, 3, 4} with a matrix (with the elements of this

set listed in increasing order).

A. {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

B. {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}