Consider (10+2z)/(6+z) = 2. A. Tell whether the given equation is true when cons
ID: 3403435 • Letter: C
Question
Consider (10+2z)/(6+z) = 2. A. Tell whether the given equation is true when considered as an existential statement. B. Tell whether the given equation is true when considered as a universal statement. C. Justify your answers to part a and b. Consider (10+2z)/(6+z) = 2. A. Tell whether the given equation is true when considered as an existential statement. B. Tell whether the given equation is true when considered as a universal statement. C. Justify your answers to part a and b. A. Tell whether the given equation is true when considered as an existential statement. B. Tell whether the given equation is true when considered as a universal statement. C. Justify your answers to part a and b.Explanation / Answer
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.