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Assignment 2

This document is an assignment for the Discrete Structures & Theory of Logic course at GL Bajaj Institute of Technology & Management. It includes a series of questions related to functions, Boolean expressions, and logic simplifications that students are required to solve. The assignment is structured to assess various levels of understanding as indicated by Bloom's taxonomy.

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19 views1 page

Assignment 2

This document is an assignment for the Discrete Structures & Theory of Logic course at GL Bajaj Institute of Technology & Management. It includes a series of questions related to functions, Boolean expressions, and logic simplifications that students are required to solve. The assignment is structured to assess various levels of understanding as indicated by Bloom's taxonomy.

Uploaded by

Lucky Sharma
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Greater Noida

GL BAJAJ
Institute of Technologies & Management
[Approved by AICTE, Govt. of India & Affiliated to Dr. APJ
Abdul Kalam Technical University, Lucknow, U.P., India]
Department of Computer Science & Engineering (AI)

Assignment 2
Subject: Discrete Structures & Theory of Logic Subject Code: (BCS303)
Faculty Name: Zarrish Iqrar Class: AI-1 & AI-2
Year/Sem: 2nd Yr / 3rd Session: 2025-26
S.no Question Blooms Level
1. If f : A → B, g : B → C are invertible functions, then show that g ο f: A BCS303.2, K4
→ C is invertible and (g o f)–1 = f–1 ο g–1.

2. Find the domain and range of the real function f defined by f(x) = |x- BCS303.2, K2
1|.
3. State whether the function f: N→ N given by f(x) = 5x is injective, surjective BCS303.2
or both. K4
4. Determine whether each of these functions is a bijective from R to R BCS303.2 K3
a. f(x) = (x^3 + 2x)/x
b. f(x) = 2/x
5. Draw Karnaugh map and simplify the Boolean expression: - BCS303.2, K2
a. A’B’C’D’+ A’B C’ D + A’ B’ C D + A’B’C D’ + A’B C D
b. F(ABCD)=Σ(0,1,2,3,4,5,6,7,8,9,11), also draw a logic
diagram.
6. Define a Boolean function of degree n. Simplify the following Boolean BCS303.2, K1
expression using Karnaugh maps
F(w, x, y, z) = Σ (w’xy + xy'z + x'y'z + x'yz + x'y'z')

7. Consider the Boolean function. BCS303.2, K4


f(x1, x2, x3, x4) = x1 + (x2. (x1′ + x4) + x3. (x2′ + x4′))
a. Simplify f algebraically
b. Draw the logic circuit of the f and the reduction of the
f.
8. Using Boolean identities, reduce the given Boolean expression: BCS303.2, K1
a. F(X, Y, Z) = X′Y + YZ′ + YZ + XY′Z′
b. F(P ,Q, R)=(P+Q)(P+R)
9. Illustrate the following composition functions if f: R→ R, g: R→ R, and h: BCS303.2, K4
R→ R defined by f(x)= 3x^2 + 2, g(x)= 7x -5 and h(x) = 1/x ,
(i). (fogoh)(x) (ii). (gog)(x) (iii). (goh)(x) (iv). (hogof)(x)
10. Using Boolean algebra show that BCS303.2, K2
(i). (f + g’) (f + h’) (g + h) = f (g + h)
(ii). h (f + g)’ + f’gh = f’h

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