MTH105: Fundamentals of Mathematics Assignment, SUSS, Singapore A set of premises is given below. Determine which of the following statements is a valid conclusion
Question 1
- A set of premises is given below
(𝑝 ⟶ 𝑞) ∨ (~𝑟)
(~𝑝) ∧ (𝑞 ∨ 𝑟)
𝑟 ⟶ (~𝑝)
Determine which of the following statements is a valid conclusion from the above set of premises using truth tables or by providing a logical explanation.
(~ 𝑝) ∨ (~𝑟)
𝑞 ⟶ (𝑝 ∧ (~𝑞))
𝑝 ⟶ (𝑞 ∧ ~𝑟)
- Construct a chain of logical equivalences to show that
(~𝑞 ∧ 𝑟) ⟶ (𝑝 ⟶ 𝑞) ≡ (~𝑞) ⟶ (𝑝 ⟶ ~𝑟).
Do not use truth tables in this part of the question.
- Use the Rules of Inference to prove that the following argument form is valid.
𝑞 ∨ 𝑟
(𝑝 ∧ 𝑞) ⟶ s
~ s
∴ 𝑝 ⟶ 𝑟
Do not use truth tables in this part of the question.
Question 2
- Give a counter-example to show that the following statement is false.
∀𝑥 ∈ ℕ ∀𝑦 ∈ ℝ ∀𝑧 ∈ ℝ ((𝑥2 < 𝑦2) ∨ (𝑦2 < 𝑧2)) ⟶ ((𝑥 < 𝑦) ∨ (𝑦 < 𝑧))
- Provide the negation of the statement, giving your answer without using any logical negation symbol. Equality and inequality symbols such as =, ≠, <, > are allowed.
∃𝑥 ∈ ℤ ∀𝑦 ∈ ℕ ∀𝑧 ∈ ℕ ((𝑥 ≠ 0) ∧ (𝑥𝑦)𝑧 = 1) ⟶ ((𝑧 = 0) ∨ (𝑥𝑦 = 1))
- Let 𝐷 be the set
𝐷 = {−10, −9, −7, −6, −4, −3, −2,0,1,2,3,4,5,6,9,10,12,13,14}.
Suppose that the domain of the variable 𝑥 is 𝐷. Write down the truth set of the predicate.
((𝑥 > 1) ⟶ (𝑥 is even)) ⟶ (𝑥 is divisible by 4).
- Let 𝑃,𝑄, 𝑅, 𝑆 denote predicates. Use the Rules of Inference to prove that the following argument form is valid.
∀𝑥 (𝑃(𝑥) ⟶ (∀𝑦 𝑄(𝑦)))
∀𝑥 (𝑅(𝑥) ⟶ (∃𝑦 ~𝑄(𝑦)))
∃𝑥 (𝑅(𝑥) ∧ 𝑆(𝑥))
∴ ∀𝑥 ~𝑃(𝑥)
Stuck with a lot of homework assignments and feeling stressed ? Take professional academic assistance & Get 100% Plagiarism free papers
Explore top-notch Do My Assignment services at Singapore University of Social Science through Online Assignment Experts. Elevate your grades with Tutor Marked Assignments through My Assignment Help SG. Get ready to excel in MTH105: Fundamentals of Mathematics effortlessly.
- ECE316 ECA: Classroom Inquiry and Action Research: A Research-Based Assessment
- BPM115 TMA02: Sustainable Materials Feasibility Study for a Cross-Country Bridge
- BSC203 Assignment: Project Management Portfolio: Key Deliverables and Lessons Learned
- SOC367 ECA: Impact on Gender Equality in the Philippines and Southeast Asia
- HBC251 ECA: Religion in Contemporary Societies Semester 2025 SUSS
- HRM335 ECA: Analysis of Thought Leadership: Influence, Impact, and Competency Framework
- HBC101 TMA01: Understanding Contemporary Society: The Social and Behavioural Sciences
- HRM358 ECA: Diversity and Inclusion in the Workplace Semester 2025
- BUS356 Group Assignment: Contemporary Financial Accounting
- BUS357 ECA: Starting and Managing a Business Semester 2025
UP TO 15 % DISCOUNT