Please complete the following exercises:Express using English.p: “The election is decided” andq: “The votes have been counted,”a) q → p’b) p’ → q Use a truth table to verify the ﬁrst De Morgan law (p ∧ q)’ ≡ p’ ∨ q’. Suppose that the domain for x consists of all English text.P(x):“x is a clear explanation,”Q(x): “x is satisfactory,” andR(x):“x is an excuse,” Express each of these statements using quantiﬁers, logical connectives, and P (x), Q(x),and R(x). a) Some clear explanations are satisfactoryb) All excuses are unsatisfactoryc) Some excuses are not clear explanations.d) Does (c) follow from (a) and (b)? Prove that if you pick four utensils from a drawer containing just spoons, forks, and knives, you must get either a pair of forks or a pair of spoons or a pair of knives. Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or non-constructive? Prove that 4n < ?! if n is an integer greater than 8.

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Description: Please complete the following exercises:Express using English.p: “The election is decided” andq: “The votes have been counted,”a) q → p’b) p’ → q Use a truth table to verify the ﬁrst De Morgan law (p ∧ q)’ ≡ p’ ∨ q’. Suppose that the domain for x c

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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 complete the following exercises:

Express using English.

p: “The election is decided” and

q: “The votes have been counted,”

a) q → p’
b) p’ → q

Use a truth table to verify the ﬁrst De Morgan law (p ∧ q)’ ≡ p’ ∨ q’.

Suppose that the domain for x consists of all English text.

P(x):“x is a clear explanation,”

Q(x): “x is satisfactory,” and

R(x):“x is an excuse,”

Express each of these statements using quantiﬁers, logical connectives, and P (x), Q(x),and R(x).

a) Some clear explanations are satisfactory
b) All excuses are unsatisfactory
c) Some excuses are not clear explanations.
d) Does (c) follow from (a) and (b)?

Prove that if you pick four utensils from a drawer containing just spoons, forks, and knives, you must get either a pair of forks or a pair of spoons or a pair of knives.

Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or non-constructive?

Prove that 4n < ?! if n is an integer greater than 8.

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