The number of choices of Delta in {wedge, vee | vedclass

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

Question

(B) Let $S$ be the statement $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$.We test each operator for $\Delta$:$1$. If $\Delt

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Let $S$ be the statement $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$.We test each operator for $\Delta$:$1$. If $\Delta = \wedge$: $(p \wedge q) \Rightarrow ((p \wedge \sim q) \vee (\sim p \wedge q))$. This is not a tautology (e.g.,if $p=T, q=T$,then $T \Rightarrow (F \vee F) = F$).$2$. If $\Delta = \vee$: $(p \vee q) \Rightarrow ((p \vee \sim q) \vee (\sim p \vee q))$. This simplifies to $(p \vee q) \Rightarrow (T) = T$,which is a tautology.$3$. If $\Delta = \Rightarrow$: $(p$ $\Rightarrow q)$ $\Rightarrow ((p$ $\Rightarrow \sim q) \vee (\sim p$ $\Rightarrow q))$. If $p=T, q=T$,then $(T$ $\Rightarrow T)$ $\Rightarrow ((T$ $\Rightarrow F) \vee (F$ $\Rightarrow T)) = T$ $\Rightarrow (F \vee T) = T$ $\Rightarrow T = T$. If $p=T, q=F$,then $(T$ $\Rightarrow F)$ $\Rightarrow ((T$ $\Rightarrow T) \vee (F$ $\Rightarrow F)) = F$ $\Rightarrow (T \vee T) = T$. If $p=F, q=T$,then $(F$ $\Rightarrow T)$ $\Rightarrow ((F$ $\Rightarrow F) \vee (T$ $\Rightarrow T)) = T$ $\Rightarrow (T \vee T) = T$. If $p=F, q=F$,then $(F$ $\Rightarrow F)$ $\Rightarrow ((F$ $\Rightarrow T) \vee (T$ $\Rightarrow F)) = T$ $\Rightarrow (T \vee F) = T$. Thus,it is a tautology.$4$. If $\Delta = \Leftrightarrow$: $(p \Leftrightarrow q) \Rightarrow ((p \Leftrightarrow \sim q) \vee (\sim p \Leftrightarrow q))$. If $p=T, q=T$,then $(T \Leftrightarrow T)$ $\Rightarrow ((T \Leftrightarrow F) \vee (F \Leftrightarrow T)) = T$ $\Rightarrow (F \vee F) = F$. Not a tautology.Therefore,there are $2$ choices: $\vee$ and $\Rightarrow$.

The number of choices of $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$,such that $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$ is a tautology,is

Similar Questions

Which of the following sentences are statements? Give reasons for your answer.
"Answer this question."

Rewrite the following statement in the form "$p$ if and only if $q$":
For you to get an $A$ grade,it is necessary and sufficient that you do all the homework regularly.

$\sim (p \Rightarrow q) \Leftrightarrow \sim p \vee \sim q$ is

Negation of the compound proposition: "If the examination is difficult,then $I$ shall pass if $I$ study hard."

Vedclass Test Series

Exam Paper Generator

Online Exam Module