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Exam 2 mathematic tooks for Computer science- Math 180, Exams of Mathematics

University of Rhode Island (URI)Mathematics
Prof. Madhav Sharma

a past exam for you to use in case you need guidance

Typology: Exams

2022/2023

Uploaded on 07/09/2023

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paola-sustache 🇺🇸

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MTH 180 Math Tools for Computing - Summer 2023
Exam 1 (Sec 1.2, 6.1, 1.3, 2.1, and 2.2)
Due: Monday, 7/3
Name: Score: /50
URI ID: Instructions:
- Show your complete work. A correct final answer without supporting work receives no partial
credits.
- You may use lecture notes and our textbook but must not receive any help from other re-
sources.
1. (5 points) Describe the following set using set-roster notation.
(a) S={m∈Z| − 2≤m < 3}
(b) T={m∈Z+|m= 1 + 2(−1)i, for some integer i}
2. (5 points) Let A={2,4}and B={u, r, i}. Find A×B. How many elements are there in
A×B?
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Download Exam 2 mathematic tooks for Computer science- Math 180 and more Exams Mathematics in PDF only on Docsity!

MTH 180 Math Tools for Computing - Summer 2023

Exam 1 (Sec 1.2, 6.1, 1.3, 2.1, and 2.2)

Due: Monday, 7/

Name: Score: /

URI ID: Instructions:

  • Show your complete work. A correct final answer without supporting work receives no partial credits.
  • You may use lecture notes and our textbook but must not receive any help from other re- sources.
  1. (5 points) Describe the following set using set-roster notation. (a) S = {m ∈ Z| − 2 ≤ m < 3 }

(b) T = {m ∈ Z+|m = 1 + 2(−1)i, for some integer i}

  1. (5 points) Let A = { 2 , 4 } and B = {u, r, i}. Find A × B. How many elements are there in A × B?
  1. (5 points) Let A = { 1 , 3 , 5 , 7 , 9 }, B = { 3 , 6 , 9 }, and C = { 2 , 4 , 6 , 8 }. Find (a) A ∩ B

(b) A ∪ C

(c) C − B

  1. (5 points) Let A = {n ∈ Z|n = 5r for some integer r} and B = {m ∈ Z|m = 20s for some integer s}. Prove that B ⊆ A.
  1. (5 points) Write truth table for the statement form p ∧ (¬p ∨ q).

(¬p means the negation of p)

  1. (5 points) Use De Morgan’s laws to write the negation for the following statement.

This computer program has a logical error or it is being run with an incomplete data set.

  1. (5 points) Use truth table to verify that the following statements are logically equivalent.

¬(p → q) ≡ p ∧ ¬q

  1. (5 points) Rewrite the following statement in ”if-then” form in two ways, one of which is contraposition of other. Being divisible by 3 is necessary condition for this number to be divisible by 9.