Problem 1: Section 2.2, Exercise 8 8. If P and Q are statements, is the statement (PVQ)^(P ^ Q) logically equivalent to the statement (PA-Q) v(Q^-P)? Justify your conclusion.
Problem 1: Section 2.2, Exercise 8 8. If P and Q are statements, is the statement (PVQ)^(P ^ Q) logically equivalent to the statement (PA-Q) v(Q^-P)? Justify your conclusion.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Problem 1: Section 2.2, Exercise 8
8. If P and Q are statements, is the statement (P ✓ Q) ^¬ (P ^ Q) logically
equivalent to the statement (P^-Q)v(Q ^¬P)? Justify your conclusion.
![Problem 4: Section 2.4, Exercise 3
3. For each of the following statements
• Write the statement as an English sentence that does not use the sym-
bols for quantifiers.
• Write the negation of the statement in symbolic form in which the nega-
tion symbol is not used.
• Write a useful negation of the statement in an English sentence that
does not use the symbols for quantifiers.
* (a) (3x € Q) (x > √2).
(b) (Vx = Q) (x² −2 = 0).
* (c) (Vx € Z) (x is even or x is odd).
(d) (3x € Q) (√2 < x < √
actually a conjunction. It means √√2 < x and x <√3.
66
√3). Note: The sentence “√2 < x < √√3" is
* (e) (Vx € Z) (If x² is odd, then x is odd).
(f) (Vn € N) [If n is a perfect square, then (2" – 1) is not a prime num-
ber].
(g) (\n € N) (n² — n +41 is a prime number).
* (h) (3x € R) (cos(2x) = 2(cosx)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F916b3e43-3e70-4159-b0c4-23957999f35d%2Ff0e2c856-2e8a-482f-a027-8f61c2361907%2Fzexn6q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 4: Section 2.4, Exercise 3
3. For each of the following statements
• Write the statement as an English sentence that does not use the sym-
bols for quantifiers.
• Write the negation of the statement in symbolic form in which the nega-
tion symbol is not used.
• Write a useful negation of the statement in an English sentence that
does not use the symbols for quantifiers.
* (a) (3x € Q) (x > √2).
(b) (Vx = Q) (x² −2 = 0).
* (c) (Vx € Z) (x is even or x is odd).
(d) (3x € Q) (√2 < x < √
actually a conjunction. It means √√2 < x and x <√3.
66
√3). Note: The sentence “√2 < x < √√3" is
* (e) (Vx € Z) (If x² is odd, then x is odd).
(f) (Vn € N) [If n is a perfect square, then (2" – 1) is not a prime num-
ber].
(g) (\n € N) (n² — n +41 is a prime number).
* (h) (3x € R) (cos(2x) = 2(cosx)).
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