Show that (p→q)→(r→s) and (p→r)→(q→s) are not logically equivalent or not? I've done some work but got stuck on it. You may explain the answer differently if I worked on the question incorrectly.
Show that (p→q)→(r→s) and (p→r)→(q→s) are not logically equivalent or not? I've done some work but got stuck on it. You may explain the answer differently if I worked on the question incorrectly.
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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Show that (p→q)→(r→s) and (p→r)→(q→s) are not logically equivalent or not?
I've done some work but got stuck on it. You may explain the answer differently if I worked on the question incorrectly.
Transcribed Image Text:Caye 2: LHS # RHS Find such
pair vabues"
TE F
LHS
RH'S
(r→r)→(eう5)
Assume (p>e)+(r>s)=T Assume (p>r) (5)= F
Ta F=F
If aTrand 5=F
(P+7) > (r→F)=T s0,q=T and sEF
50,9T and SEF
So, r:T else ifFF
then
Expert Solution
Step 1
We have
Now, two statements are said to be logically equivalent if we make truth tables for both of them and the truth tables are identical for all possible truth values.
Now, we make the truth table:
| F | F | F | F | T | T | T | T | T | T |
| F | F | F | T | T | T | T | T | T | T |
| F | F | T | F | T | F | T | T | F | T |
| F | F | T | T | T | T | T | T | T | T |
| F | T | F | F | T | T | T | F | T | F |
| F | T | F | T | T | T | T | T | T | T |
| F | T | T | F | T | F | T | F | F | F |
| F | T | T | T | T | T | T | T | T | T |
| T | F | F | F | F | T | F | T | T | T |
| T | F | F | T | F | T | F | T | T | T |
| T | F | T | F | F | F | T | T | T | T |
| T | F | T | T | F | T | T | T | T | T |
| T | T | F | F | T | T | F | F | T | T |
| T | T | F | T | T | T | F | T | T | T |
| T | T | T | F | T | F | T | F | F | F |
| T | T | T | T | T | T | T | T | T | T |
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