Computer Science
Determine whether the given expression is valid or not:
(p ⇒ q) ⇒ [~q ⇒ (~p^~q)]
Boolean Algebra
5 Likes
Answer
| p | q | ~p | ~q | p⇒q | ~p^~q | ~q⇒(~p^~q) | (p⇒q) ⇒ [~q⇒ (~p^~q)] |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
As the expression is a tautology hence, it is a valid expression.
Answered By
2 Likes
Related Questions
Let X=1 represents "you work hard" and 0 otherwise.
Let Y=1 represents "you succeed" and 0 otherwise.
Using the information given above, construct:
(i) the truth table and
(ii) the logical expression for the following statement:
"If and only if you work hard you succeed".Draw the truth table to prove the following proportional expression:
a ⇒ b = (a ⇒ b) . (b ⇒ a)
Differentiate between a tautology and a contradiction.
Using the truth table verify the expression
(~P ⇒ Q) ^ P = (P ^ ~Q) v (P ^ Q)