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• 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
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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• 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.
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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