Construct a truth table to decide if the two statements are equivalent. 21) -p a -q; ~(p v q) A) True 21) B) False Tell whether the statement is true or false. 22) 7 « (14, 21, 28, 35, 42} A) True 22) B) False Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let A = {n « N[ n > 50} B = {n « N] n < 250} O= {n « N] n is odd} E = {n « N[ n is even} 23) A' ^ B' A) disjoint 23) B) not disjoint
Construct a truth table to decide if the two statements are equivalent. 21) -p a -q; ~(p v q) A) True 21) B) False Tell whether the statement is true or false. 22) 7 « (14, 21, 28, 35, 42} A) True 22) B) False Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let A = {n « N[ n > 50} B = {n « N] n < 250} O= {n « N] n is odd} E = {n « N[ n is even} 23) A' ^ B' A) disjoint 23) B) not disjoint
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The image is a section from an educational document on logic and set theory, containing exercises with multiple-choice answers and logic tables.
**Logic Tables:**
- Two tables are provided for truth evaluation:
1. Table C has columns labeled `p`, `q`, and `(~p ∧ ~q)`.
- Rows show various combinations of truth values (T for true, F for false) and their outcomes.
2. Table D also features columns for `p`, `q`, and `(~p ∧ ~q)`.
- Similar row structure with different entries than Table C.
**Question 21:**
"Construct a truth table to decide if the two statements are equivalent."
- Expression: ~p ∧ ~q ⋅ ~(p ∨ q)
- Two answer choices: A) True, B) False
- Blank space for answer.
**Question 22:**
"Tell whether the statement is true or false."
- Verification: 7 ∈ {14, 21, 28, 35, 42}
- Two answer choices: A) True, B) False
- Blank space for answer.
**Set Theory Section:**
- Instruction: Determine whether the given set is disjoint or not disjoint.
- Definition of sets with the universal set N (positive integers):
- A = {n ∈ N | n > 50}
- B = {n ∈ N | n < 250}
- O = {n ∈ N | n is odd}
- E = {n ∈ N | n is even}
**Question 23:**
"Determine if A' ∩ B' is disjoint."
- Two answer choices: A) Disjoint, B) Not disjoint
- Blank space for answer.
**Question 24:**
"Provide an appropriate response."
"Which of the following is NOT a subset of the set {p, o, 7}?"
- Four options:
A) ∅
B) {o, 7}
C) {p, o, 7}
D) 7
- Blank space for answer.
The tasks involve evaluating logical statements and understanding set operations, requiring a grasp of truth tables and subset definitions.
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