Necessary condition

y = f(x) ∧ y = g(x) ⇒ 2y = f(x) + g(x)

 

 

Example:

y = x² ∧ y = -x² + 1  ⇒ y = 1/2

 

cf.

[i]

y = f(x) ∧ y = g(x) ⇔ 2y = f(x) + g(x) ∧ 0 = f(x) - g(x)

 

[ii]

f(x,y) = 0 ∧ f(y,x) = 0 ⇔  f(x,y) + f(y,x) = 0 ∧ f(x,y) - f(y,x) = 0

 

[iii]

f(x,y)=0 ∧ g(x,y)=0 ⇒ ∃k ( f(x,y) + kg(x,y)=0 )

 

[iv]

f(x,y)=0 ∧ g(x,y)=0 ⇔ ∀k ( f(x,y) + kg(x,y)=0 )

 

[v]

y=ax²+bx+c ∧ y=px²+qx+r ⇒ (p-a)y=(pb-aq)x+(pc-ar)

 

[vi]

x²+y²+ax+by+c=0 ∧ x²+y²+px+qy+r=0 ⇒ (a-p)x+(b-q)y+(c-r)=0