+1 vote
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Akash, Bharani, Chetan and Deepa are invited to a party. If Bharani and Chetan attend, then Deepa will attend too. If Bharani does not attend, then Akash will not attend. If Deepa does not attend, which of the following is true?

1. Chetan does not attend
2. Akash does not attend
3. either (A) or (B)
4. none of the above

recategorized | 61 views

Let

Akash attends the party $=A$,

Bharani attends the party $=B$ ,

Chetan attends the party $=C$,

Deepa attends the party $=D$.

If (Bharani and Chetan) attends the party $\implies$ Deepa attends the party is true

$\equiv (B \wedge C) \implies D$ is true

$\equiv \sim D \implies \sim (B \wedge C)$ is true

$\equiv \sim D \implies \sim B\ \vee \sim C$ is true

$\equiv$ If Deepa does not attends the party then {either (Bharani will also not attend the party) OR  (Chetan will also not attend the party)}.......$(i)$

If Bharani does not attend $\implies$ Akash Does not attend the party............$(ii)$

From $(i)$ and $(ii)$

Since it is given Deepa does not attends the party

so Bharat OR Chetan also do not attend the party.

and if Bharat does not attends the party then Akash also do not attends the party.

Hence Either Akash and Bharani would not be able to attend the party OR Chetan would not be able to attend the party

So option $C.$ is the correct choice.
by Boss (25.1k points)
edited by
+1

∼D⟹∼(B∧C) is true

If Deepa does not attends the party then Bharat and Chetan will also not attend the party

∼D⟹∼(B∧C)  ≡  ∼D⟹(∼B v∼C) but not as you think !

0
so what is the statement for $\sim (B \wedge C)$ ?
0
both not at a time come

Suppose,

$A$ means Akash attends the party

$B$ means Bharani attends the party

$C$ means Chetan attends the party

$D$ means Deepa attends the party

Now, according to given questions :-

$B\wedge C \rightarrow D \\ \sim B \rightarrow \;\sim A$

$\sim D \rightarrow \; ?$

Here,

$B\wedge C \rightarrow D$  is equivalent to $C \wedge \sim D \rightarrow \sim B$

Now, from $C \wedge \sim D \rightarrow \sim B$ and $\sim B \rightarrow \;\sim A$

$C \wedge \sim D \rightarrow \sim A$

and it is equivalent to $A \wedge C \rightarrow D$ which is also equivalent to $\sim D \rightarrow \sim A \vee \sim C$