GATE CSE
First time here? Checkout the FAQ!
x
0 votes
223 views

asked in Mathematical Logic by Boss (6.8k points)  
retagged by | 223 views
All are invalid
Please explain why
@arjun sir,pls help in this one.
sorry, I dont want to boil my brain solving such questions. For mathematical logic there are numerous previous year questions and also many PDFs are given in gatecse. When all those are there I do not want to waste time decoding such poorly formatted questions.
i understand arjun sir,but if u colud just tell which option is correct then that would have helped..!

thanks anyway :-)
^That means you did not understand :(

1 Answer

+1 vote
Statement 1)

Let the domain be set of real numbers.

B: true

A: number is integer

LHS = false and RHS= true

So, fale double implies true is false.

 

Statement 2)

Let the domain be set of real numbers.

B: false

A: number is integer

LHS = true and RHS= false

So, true double implies false is false.
answered by Veteran (15.5k points)  
Just notice the difference here:

Vx B -> A(x)

 and

Vx B  -> Vx A(x)

did you get it?
@sushant,yes,i have gone through the above link and see in that one 3rd statment is true.

meanwhile i understood that statement 1 is incorrect but

for statement 2,i was thinking that as B is already true then whether it is for some A to be true or for all A to be true,it is true afterall as it is universal.i guess i am wrong only.:-(

THanks for helping out!

3rd statment is wrong na??
Lhs

= $\exists$x( A(x) -> B(x) )

= $\exists$x( ~A(x) V B(x) )

= $\exists$x ~A(x)  V  $\exists$x B(x)

= Vx A(x)   V   $\exists$x B(x)

= RHS

So, true.
Also try using example.
thanks sushant,

if i take one example,we take domain as {3,6,9}

A=div by 2 and B = div by 3

then RHS is obviously TRue but what about LHS --∃x( A(x) -> B(x) ) as here,A is not true for anyone.so LHS is true or false/?
x=6, A is true and B is true. So, LHS=true
sorry,domain is {3,9,15},,then tell for LHS.
Yes, u got it :)
thanks sushant..:-)


Top Users Sep 2017
  1. Habibkhan

    8796 Points

  2. rishu_darkshadow

    3572 Points

  3. Warrior

    2914 Points

  4. Arjun

    2840 Points

  5. A_i_$_h

    2550 Points

  6. manu00x

    2268 Points

  7. nikunj

    1990 Points

  8. Bikram

    1874 Points

  9. makhdoom ghaya

    1820 Points

  10. SiddharthMahapatra

    1718 Points


26,346 questions
33,928 answers
80,525 comments
31,231 users