Question
Download Solution PDFThe Boolean expression ~(p ⇒ (~q)) is equivalent to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFrom question, the Boolean expression given is:
~(p ⇒ (~q))
The truth table for the above expression is given below:
|
p |
q |
~q |
P ⇒ (~q) |
~(p ⇒ (~q)) |
|
T |
T |
F |
F |
T |
|
T |
F |
T |
T |
F |
|
F |
T |
F |
T |
F |
|
F |
F |
T |
T |
F |
Now, we need to consider the options:
Option (a) p ∧ q:
|
p |
q |
P ∧ q |
|
T |
T |
T |
|
T |
F |
F |
|
F |
T |
F |
|
F |
F |
F |
Option (b) q ⇒ ~p:
|
p |
q |
~p |
q ⇒ ~p |
|
T |
T |
F |
F |
|
T |
F |
F |
F |
|
F |
T |
T |
T |
|
F |
F |
T |
T |
Option (c) p ∨ q:
|
p |
q |
P ∨ q |
|
T |
T |
T |
|
T |
F |
T |
|
F |
T |
T |
|
F |
F |
F |
Option (d) (~p) ⇒ q:
|
p |
q |
~p |
(~p) ⇒ q |
|
T |
T |
F |
T |
|
T |
F |
F |
T |
|
F |
T |
T |
T |
|
F |
F |
T |
F |
On comparing the truth values of expression and truth values in options. The truth values in option is same and option (a) is the correct answer.
Last updated on Jul 11, 2025
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