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Please help me with these question. I am having trouble understanding what to do. Just complete  d) for question 4

Please help me with these question. I am having trouble understanding what to do. Just complete  d) for question 4

Advanced Engineering Mathematics
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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Please help me with these question. I am having trouble understanding what to do.

Just complete 

d) for question 4 &

b) for question 5

4. Suppose T is a set of natural numbers, and we have the following statement about T. S₁: 2 is the only prime number that divides elements of T. Which of the following statements imply S₁? Which are implied by S₁? For each case, give a brief justification. (a) S₂: T is the set of all natural numbers that satisfy the quadratic equation z² + x + 1 = 0. (b) Ss: T= {16, 8, 528}. (c) S4: All elements of T are equal to 2", where n is a natural number. (d) S5: If i, jT, and i<j, then i divides j.
Transcribed Image Text:4. Suppose T is a set of natural numbers, and we have the following statement about T. S₁: 2 is the only prime number that divides elements of T. Which of the following statements imply S₁? Which are implied by S₁? For each case, give a brief justification. (a) S₂: T is the set of all natural numbers that satisfy the quadratic equation z² + x + 1 = 0. (b) Ss: T= {16, 8, 528}. (c) S4: All elements of T are equal to 2", where n is a natural number. (d) S5: If i, jT, and i<j, then i divides j.
5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you must clearly state which rule you apply. (a) ((PQ₁) ^ (P⇒ Q2)) ⇒(P⇒ (Q₁ ^ Q₂)) (b) ((3x D, P(x) v Q(x)) = R(y)) (((3x D, P(x)) = R(y)) ^ ((3x D, Q(x)) = R(y)))
Transcribed Image Text:5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you must clearly state which rule you apply. (a) ((PQ₁) ^ (P⇒ Q2)) ⇒(P⇒ (Q₁ ^ Q₂)) (b) ((3x D, P(x) v Q(x)) = R(y)) (((3x D, P(x)) = R(y)) ^ ((3x D, Q(x)) = R(y)))
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