Please written by computer source 1) Write truth tables for the statement forms in A.∼p ∧ q B. p ∧ (q ∧ r) 2) Determine whether the statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. 1. p ∨ (p ∧ q) and p 2. p ∨ t and t 3. (p ∧ q) ∧ r and p ∧ (q ∧ r) 4. (p ∧ q) ∨ r and p ∧ (q ∨ r) 3) Assume x is a particular real number and use De Morgan’s laws to write negations for the statements 1. −2 < x < 7 2. x < 2 or x > 5 3. 1 > x ≥ −3 4) Use truth tables to establish which of the statement forms are tautologies and which are contradictions. 1. (p ∧ q) ∨ (∼p ∨ (p ∧ ∼q)) 2. (p ∧ ∼q) ∧ (∼p ∨ q) 5) In the below, a logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step. (p ∧ ∼q) ∨ (p ∧ q) ≡ p ∧ (∼q ∨ q) by (a) ≡ p ∧ (q ∨ ∼q) by (b) ≡ p ∧ t by (c) ≡ p by (d) Therefore, (p ∧ ∼q) ∨ (p ∧ q) ≡ p. 6) Use Theorem 2.1.1 to verify the logical equivalences in A and B. Supply a reason for each step. 1. (p ∧ ∼q) ∨ p ≡ p 2. ∼((∼p ∧ q) ∨ (∼p ∧ ∼q)) ∨ (p ∧ q) ≡
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A database design is the process of data organization based on a database model. The process deals with identifying what data should be stored in a database and how data elements relate to each other.
Entity Relationship Diagram
Complex real-world applications call for large volumes of data. Therefore, it is necessary to build a great database to store data safely and coherently. The ER data model aids in the process of database design. It helps outline the structure of an organization’s database by understanding the real-world interactions of objects related to the data. For example, if a school is tasked to store student information, then analyzing the correlation between the students, subjects, and teachers would help identify how the data needs to be stored.
Please written by computer source
1) Write truth tables for the statement forms in
A.∼p ∧ q
B. p ∧ (q ∧ r)
2) Determine whether the statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence.
1. p ∨ (p ∧ q) and p
2. p ∨ t and t
3. (p ∧ q) ∧ r and p ∧ (q ∧ r)
4. (p ∧ q) ∨ r and p ∧ (q ∨ r)
3) Assume x is a particular real number and use De Morgan’s laws to write negations for the statements
1. −2 < x < 7
2. x < 2 or x > 5
3. 1 > x ≥ −3
4) Use truth tables to establish which of the statement forms are tautologies and which are contradictions.
1. (p ∧ q) ∨ (∼p ∨ (p ∧ ∼q))
2. (p ∧ ∼q) ∧ (∼p ∨ q)
5) In the below, a logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step.
(p ∧ ∼q) ∨ (p ∧ q) ≡ p ∧ (∼q ∨ q) by (a)
≡ p ∧ (q ∨ ∼q) by (b)
≡ p ∧ t by (c)
≡ p by (d)
Therefore, (p ∧ ∼q) ∨ (p ∧ q) ≡ p.
6) Use Theorem 2.1.1 to verify the logical equivalences in A and B. Supply a reason for each step.
1. (p ∧ ∼q) ∨ p ≡ p
2. ∼((∼p ∧ q) ∨ (∼p ∧ ∼q)) ∨ (p ∧ q) ≡
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