Consider 102z6z 2 A Tell whether the given equation is true

Solution

Consider the given statement :

(10+2z)/(6+z) = 2.

(A) If we take z =2 then (10 + 2z ) /(6 + z ) = (10 + 2(3))/(6+3) = 18/9 =2

Thus there exists a z = 2 that satisfies the equation (10+2z)/(6+z) = 2.

hence the given equation is true when considered as an existential statement.

(B) If we take z =1 then (10 + 2z ) /(6 + z ) = (10 + 2(1))/(6+1) = 12/7 2

Thus for all z the equation does not satisfy the equation (10+2z)/(6+z) = 2.

hence the given equation is false when considered as an universal statement.