2.3k views

Consider the following statements:

• P: Good mobile phones are not cheap
• Q: Cheap mobile phones are not good

L: P implies Q
M: Q implies P
N: P is equivalent to Q

Which one of the following about L, M, and N is CORRECT?

1. Only L is TRUE.
2. Only M is TRUE.
3. Only N is TRUE.
4. L, M and N are TRUE.
edited | 2.3k views

Lets break the given compound statements into atomic statements.

• A : Good mobile phones.
• B : Cheap mobile phones.

$P :(A\to \neg B) \iff (\neg A\vee \neg B)$
$Q :(B\to \neg A) \iff \big((\neg B\vee \neg A) \iff \neg A\vee \neg B)\big)$ (Disjunction is commutative),
Hence, $(P\iff Q)$ which means $(P\to Q)$ and $(Q \to P).$

edited
+5
Nice Explanation
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@Arjun sir

How to break this statement  into conditional statement ??

• P: Good mobile phones are not cheap
• Q: Cheap mobile phones are not good
+6

This might help ....

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Crystal clear....thqqq
+1
P and Q are contrapositives of each other.
P and Q are contra-positives to each other. A proposition and its contra-positive are always equivalent.

Equivalent and <--> are same, so p <--> q holds.

So option D)
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can you please explain me the line "P is equivalent to Q, which means P implies Q ,and Q implies P" .

P implies Q means P->Q  and Q implies P means Q->P then how can we conclude these two from the fact that P is equivalent to Q.
+1
P is equivalent to Q means (P->Q)^(Q->P). So both (P->Q) and (Q->P) must be true to ensure this.

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