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asked in Mathematical Logic by Boss (7.3k points)
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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 (18k 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..:-)


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