• 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?
• 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?
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:• 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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