MadeEasy Subject Test: Engineering Mathematics - First Order Logic

Question

#plz explain 1st and 2nd ???

Comments

is B is a free variable in statement 1??

Answer 1

A1:  

Assume B=true

             A= {false, true, false}

So, LHS = false and RHS=true

So, invalid.

 

A2:

Lets consider there 2 variables in domain viz. x1 and x2

So, LHS

= (A(x1) + A(x2)) $\rightarrow$ B

= (A(x1) + A(x2))'  + B

= (A'(x1) . A'(x2)) + B

= (A'(x1) + B) . (A'(x2) + B)

= (A(x1)$\rightarrow$ B) . (A(x2)$\rightarrow$ B)

= Vx (A(x) $\rightarrow$ B)

= RHS

 

So, this is suficient to get to options.