GATE PREV

Question

∃x(p(x)∧q(x))⟹(∃xp(x)∧∃xq(x))

a)It is false because ∃ is not distributive over ∧

b) If we say LHS is false ,then then entire statement is true.

WHICH ONE I CHOOSE ?

Comments

Answer is B.

If LHS is false, RHS will also be false. And false implies false is True

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But "∃ is not distributive over ∧" is also true ?

Answer 1

a may be false because ∃x(p(x)∧q(x)) here the vale of x is for both p(x)^q(x)

for

∃x(p(x)∧q(x))

at x=1  => p(1) and  q(1)

at x=9 =>P(9) and q(9)

.

.

.

.

at x=n => p(n) and q(n)

 

 

now for

(∃xp(x)∧∃xq(x))

vale of x is distinct for both

p(1) and  q(6)

p(6) and q (45)

.

.

.

p(n) and q(m)

 

 

so by this way it is FALSE...

 

 

correct me if i am incorrect

Comments

correct

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thanks bro