Please help solve all parts and explain answer for me. Thanks a lot. • Let p be the proposition "() is a natural number"• Let q be the proposition "The product of three consecutive numbers is divisible bythree"Letr be the proposition "The product of two consecutive numbers is divisible bytwo"(1) Suppose S = {a, b, c, d, e}. How many three-element subsets of S are there? Youranswer should be a formula, not a number.(2) By hand, use the formula and work out what the number is. Be sure to show all yourcanceling in the fraction.(3) Why is q true?(4) Why is r true?(5) Remember that (3) n(n-1)(n-2). Explain how q and r are connected to (3).=(6) Write the relationship between p, q, and r using symbolic logic.(7) What does 9 and r being true tell you about p?(8) What is another reason that p has to be true? You can use question 1 to help youfind a reason.

Answered: ● Let p be the proposition "() is a…

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 solve all parts and explain answer for me. Thanks a lot.

• Let p be the proposition "() is a natural number"
• Let q be the proposition "The product of three consecutive numbers is divisible by
three"
Letr be the proposition "The product of two consecutive numbers is divisible by
two"
(1) Suppose S = {a, b, c, d, e}. How many three-element subsets of S are there? Your
answer should be a formula, not a number.
(2) By hand, use the formula and work out what the number is. Be sure to show all your
canceling in the fraction.
(3) Why is q true?
(4) Why is r true?
(5) Remember that (3) n(n-1)(n-2). Explain how q and r are connected to (3).
=
(6) Write the relationship between p, q, and r using symbolic logic.
(7) What does 9 and r being true tell you about p?
(8) What is another reason that p has to be true? You can use question 1 to help you
find a reason.

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