CAT 1999 | Question: 123

Question

The question has a main statement followed by four statements labelled A, B, C and D. Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.

Whenever Rajeev uses the Internet, he dreams about spiders.

• A. Rajeev did not dream about spiders.
• B. Rajeev used the Internet.
• C. Rajeev dreamt about spiders.
• D. Rajeev did not use the Internet.
  1. AD
  2. DC
  3. CB
  4. DA

Answer 1

Let P=  Rajeev uses the Internet, 

     Q= he dreams about spiders.

Whenever Rajeev uses the Internet, he dreams about spiders.  which can be represt as $P\rightarrow Q$  Which is equivalent to

$Q'\rightarrow P'$

$\text{OPTION (1): AD}$  Means whenever rajeev does not dream about spiders , rajeev does not use internet which is $Q'\rightarrow P'$  so it is vaild .

$\text{Option(2): DC}$ whenever Rajeev did not use the Internet , Rajeev dreamt about spiders which is $P'\rightarrow Q$ 

SO it is not vaild 

$\text{OPTION (3): CB}$  whenever Rajeev dreamt about spiders, Rajeev used the Internet.which  is $Q\rightarrow P$

so it is not vaild .

$\text{OPTION (4):  DA}$ whenever Rajeev did not use the Internet.,Rajeev did not dream about spiders.which is $P'\rightarrow Q'$

Its also not vaild . 

hence, Answer$:(1)$