The dual of the converse of the inverse of th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Step $1$: Given statement is $S = p 	o (q 	o r)$.Step $2$: The inverse of $S$ is $∼ p 	o ∼ (q 	o r)$.Step $3$: The converse of the inverse is

Vedclass · Accepted Answer

$∼ [p \lor (r 	o q)]$

Vedclass · Answer

(A) Step $1$: Given statement is $S = p 	o (q 	o r)$.Step $2$: The inverse of $S$ is $∼ p 	o ∼ (q 	o r)$.Step $3$: The converse of the inverse is $∼ (q 	o r) 	o ∼ p$.Step $4$: Using $q 	o r \equiv ∼ q \lor r$, the expression becomes $∼ (∼ q \lor r) 	o ∼ p$, which is $(q \land ∼ r) 	o ∼ p$.Step $5$: The dual of a statement is obtained by replacing $\land$ with $\lor$, $\lor$ with $\land$, $T$ with $F$, and $F$ with $T$. The implication $A 	o B$ is $∼ A \lor B$. Thus, $(q \land ∼ r) 	o ∼ p$ is $∼ (q \land ∼ r) \lor ∼ p \equiv (∼ q \lor r) \lor ∼ p$.Step $6$: The dual of $(∼ q \lor r) \lor ∼ p$ is $(∼ q \land r) \land ∼ p$.Step $7$: Alternatively, applying the dual operation directly to the logical form: The dual of $A 	o B$ (i.e., $∼ A \lor B$) is $∼ A \land B$. Applying this to $(q \land ∼ r) 	o ∼ p$ gives $∼ (q \land ∼ r) \land ∼ p \equiv (∼ q \lor r) \land ∼ p$. Checking the options, the expression $∼ [p \lor (r 	o q)]$ is $∼ [p \lor (∼ r \lor q)] \equiv ∼ p \land (r \land ∼ q)$, which matches the dual form.

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

Similar Questions

For the circuit shown below,the Boolean polynomial is

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which of the following is a tautology?

The inverse of the proposition $(p \wedge \sim q) \Rightarrow r$ is

Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta ( p \nabla q )$ is a tautology. Then

Write the converse of the following statement:
If a number $n$ is even,then $n^{2}$ is even.

Vedclass Test Series

Exam Paper Generator

Online Exam Module