Made easy Test Series 2017 Proposition Logic

Question

Please explain in simple words as i always face problem in such type of questions-

Comments

i cant surely tell which one is valid but i can explain the statements :

for double implication ,LHS -> RHS & RHS -> LHS should satisfy

(a) LHS- if B is true for all x then A is true

     RHS - if for some x,B is true then A is true

i guess here LHS -> RHS but RHS does not imply LHS.hence not valid.

(b) LHS- if A is true for some x then B is true

      RHS -for each x,if A is true then B is true.

as here,B is not  bounded on x.so if B is true for some X then it will be true for all the x.

moreover you can take B as TRUE once and as false once and check whther LHS -> RHS and RHS -> LHS in each case.

so,acc to me ,its valid.

(c) LHS -for some x ,if A is true then B is true

     RHS - if A is true ffor all x then B is true for some x.

clearly LHS does not imply RHS.hence it is not valid

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There are maximum 3-4 types of questions possible in this topic. So, just look at previous year GATE questions and understand how they are solved. This question for example is ambiguous as so many braces are missing. Of course one could attempt it assuming some precedence rule.

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Okay Arjun Sir, thanks!!!