vx (P(x) VQ(x)) = x [~(~P(x)) v Q(x)] =vx [~P(x) → Q(x)]..... (1) Now, [~P(x) →~P(x)] [obvious] So, using the above result and (1), we get, Hy [~P(x) → (~P(x) ^ (x)) (2) We are also given that vx ((~P(x) ^ Q(x)) → R(x)) . . . . . . . (3) Then, hypothetical syllogism between (2) & (3) gives (~P(x) R(x))..... (4) Then, (4) also implies x[-R(x) →~(~P(x))] =vx [~R(x) → P(x)] Hence, proved. [contrapositive of (4)]
vx (P(x) VQ(x)) = x [~(~P(x)) v Q(x)] =vx [~P(x) → Q(x)]..... (1) Now, [~P(x) →~P(x)] [obvious] So, using the above result and (1), we get, Hy [~P(x) → (~P(x) ^ (x)) (2) We are also given that vx ((~P(x) ^ Q(x)) → R(x)) . . . . . . . (3) Then, hypothetical syllogism between (2) & (3) gives (~P(x) R(x))..... (4) Then, (4) also implies x[-R(x) →~(~P(x))] =vx [~R(x) → P(x)] Hence, proved. [contrapositive of (4)]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
EXPLAIN THIS STEP BY STEP AND WRITE DOWN EVERY RULE USED
![vx (P(x) VQ(x)) = x [~(~P(x)) v Q(x)]
=vx [~P(x) → Q(x)]..... (1)
Now, [~P(x) →~P(x)] [obvious]
So, using the above result and (1), we get,
Hy [~P(x) → (~P(x) ^ (x))
(2)
We are also given that
vx ((~P(x) ^ Q(x)) → R(x)) ....... (3)
Then, hypothetical syllogism between (2) & (3) gives
(~P(x) R(x))..... (4)
Then, (4) also implies
x[-R(x) →~(~P(x))]
= Vx [~R(x) → P(x)]
Hence, proved.
[contrapositive of (4)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45631b76-92ed-4621-943e-a0001c817b2f%2F6032b341-1919-48b2-ae15-110ca57548ed%2Fi90c1v_processed.png&w=3840&q=75)
Transcribed Image Text:vx (P(x) VQ(x)) = x [~(~P(x)) v Q(x)]
=vx [~P(x) → Q(x)]..... (1)
Now, [~P(x) →~P(x)] [obvious]
So, using the above result and (1), we get,
Hy [~P(x) → (~P(x) ^ (x))
(2)
We are also given that
vx ((~P(x) ^ Q(x)) → R(x)) ....... (3)
Then, hypothetical syllogism between (2) & (3) gives
(~P(x) R(x))..... (4)
Then, (4) also implies
x[-R(x) →~(~P(x))]
= Vx [~R(x) → P(x)]
Hence, proved.
[contrapositive of (4)]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
