3.7.5. Let P(r) be the assertion "r is positive", and let Q(r) the assertion "r >I". (a) Is the statement (Vr E R)[P(r) → Q(x)] true or false? Why? (b) Is the statement [(Vr E R)P(r)] → [(Vr E R)Q(r)] true or false? Why?
3.7.5. Let P(r) be the assertion "r is positive", and let Q(r) the assertion "r >I". (a) Is the statement (Vr E R)[P(r) → Q(x)] true or false? Why? (b) Is the statement [(Vr E R)P(r)] → [(Vr E R)Q(r)] true or false? Why?
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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Question
3.7.5 only
![(Vr)((r E S) ^ (x E T)) = (1€ U) .
(a) Write the statement SNTZU using the logic symbols (but without the symbol ).
(b) Write the statement S CTUU and its negation using the logic symbols.
3.7.5. Let P(x) be the assertion "r is positive", and let Q(r) the assertion "r>r".
(a) Is the statement (Vr E R)[P(r) → Q(r)] true or false? Why?
(b) Is the statement [(Vr € R)P(r)] → [(Vr € R)Q(r)] true or false? Why?
3.7.6. Consider the following two statements:
R= "For any real number r, there is a real number y, such that r+y<1."
S "There is a real number y, such that for all real numbers r, we have r+y<1."
(a) Write both statements using the logic symbols.
(b) Write the negations of R and S. Use the logic symbols, but do not use the symbols ' or
(c) Is R a true or a false statement? Is S a true or a false statement? Explain.
3.7.7. For what value (or values) of r ER is the following statement false? Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca102ad3-d1c6-47df-9f78-15b27813ee96%2F99ebdd2b-4344-406f-af40-36c66897a2ca%2Fz3ohe3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(Vr)((r E S) ^ (x E T)) = (1€ U) .
(a) Write the statement SNTZU using the logic symbols (but without the symbol ).
(b) Write the statement S CTUU and its negation using the logic symbols.
3.7.5. Let P(x) be the assertion "r is positive", and let Q(r) the assertion "r>r".
(a) Is the statement (Vr E R)[P(r) → Q(r)] true or false? Why?
(b) Is the statement [(Vr € R)P(r)] → [(Vr € R)Q(r)] true or false? Why?
3.7.6. Consider the following two statements:
R= "For any real number r, there is a real number y, such that r+y<1."
S "There is a real number y, such that for all real numbers r, we have r+y<1."
(a) Write both statements using the logic symbols.
(b) Write the negations of R and S. Use the logic symbols, but do not use the symbols ' or
(c) Is R a true or a false statement? Is S a true or a false statement? Explain.
3.7.7. For what value (or values) of r ER is the following statement false? Why?
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