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18 votes

What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining":

  1. If Kareena and Parineeti do not go to the shopping mall then it is not raining.
  2. If Kareena and Parineeti do not go to the shopping mall then it is raining.
  3. If it is raining then Kareena and Parineeti go to the shopping mall.
  4. If it is not raining then Kareena and Parineeti do not go to the shopping mall.
  5. None of the above.
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4 Answers

Best answer
29 votes
29 votes

Answer will be (D)

"If Kareena and Parineeti go to the shopping mall then it is raining"

Let "Kareena and Parineeti go to the shopping mall" be represented by $p$ and "it is raining" by $q$

Now, the statement says that $p→q$

  1. a. If Kareena and Parineeti do not go to the shopping mall then it is not raining.
    i.e., $\neg p→ \neg q$
    Not matching with the given implication.
  2. b.If Kareena and Parineeti do not go to the shopping mall then it is raining.
    i.e., $\neg p→ q$
    Not matching with the given implication.
  3. If it is raining then Kareena and Parineeti go to the shopping mall.
    i.e., $q→p$
    Not matching with the given implication.
  4. If it is not raining then Kareena and Parineeti do not go to the shopping mall.
    i.e., $\neg q → \neg p \equiv q \vee \neg p \equiv p→q$
    Matces with the given implication.

So, correct option is (D).

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7 votes
7 votes

p->q is equivalent with its contrapositive (Hence Option D is Ans.)

Note:-Contrapositive of p->q means converse then inverse of p->q

or inverse then converse of p->q

3 votes
3 votes

A different take on the question:

K: Kareena goes to the mall

P: Parineeti goes to the shopping mall

R: It is raining

Premise: $K \wedge P \rightarrow R$

The contrapositive of the premise is: ⌉R -> ⌉K V ⌉P

If it is not raining then Kareena does not go to the mall or Parineeti does not go to the mall.

3 votes
3 votes
Let P: Kareena go to the shopping mall

Q: Parineeti go to the shopping mall

R: It is raining

 

Now, the statement says that p ∧ q→r

so contrapositive statement would be

r’ → (p ∧ q)’

=> r’  → p’ + q’

=> If it is not raining then either Kareena did not go to the shopping mall or Parineeti did not go to the shopping mall.

therefore, Answer: E – None of the above.
Answer:

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