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(8) Let P = "(Vx ≤ R)(Jy ≤ R) (x + y > 0)”. Let Q = "(Vx € R) (Vy € R) [(xy > x) ✓ (xy < xy

(8) Let P = "(Vx ≤ R)(Jy ≤ R) (x + y > 0)”. Let Q = "(Vx € R) (Vy € R) [(xy > x) ✓ (xy < xy

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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(8) Let P = "(Vx ≤ R) (3y = R) (x + y > 0)". Let Q = “(Vx ≤ R)(√y ≤ R) [(xy > x) V (xy < y) (y)]”. (a) Is P true? Justify your answer. (b) Is Q true? Justify your answer. (c) Let R be any statement. Is (P ^ Q) R true? Justify your answer.
Transcribed Image Text:(8) Let P = "(Vx ≤ R) (3y = R) (x + y > 0)". Let Q = “(Vx ≤ R)(√y ≤ R) [(xy > x) V (xy < y) (y)]”. (a) Is P true? Justify your answer. (b) Is Q true? Justify your answer. (c) Let R be any statement. Is (P ^ Q) R true? Justify your answer.
Expert Solution
Step 1

8.

(a)  P is true.  

If  x >=0, then for any y>0, the statement P is true. If x<0, then take y=|x|+1, then x+y>0 i.e. P is true. Hence, P is a true statement. 

(b)  Q is false. 

Take  x=y=0 , then neither  (xy>x)  nor  (xy<y). Hence, Q is a false statement. 

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