Write the reciprocal and the anti-reciprocal of:
That a quadrilateral has 4 equal sides, is a necessary condition for that it is a square.
That a triangle has 2 equal sides, is a necessary condition for that it is isosceles.
Only if f is integrable in an I interval, f is continuous in I.
If an f function is derivable in a point then f is continuous in that point.
F is not an even function, to less that f(x)=f(-x).
If a<b then a^2< b^2.
To find the reciprocal of a statement, you need to negate the statement and then invert it. In mathematical terms, if the original statement is "P is a necessary condition for Q," the reciprocal would be "Q is a necessary condition for P."
1. Original statement: A quadrilateral has 4 equal sides, is a necessary condition for it to be a square.
Reciprocal: If it is a square, then it has 4 equal sides.
2. Original statement: A triangle having 2 equal sides is a necessary condition for it to be isosceles.
Reciprocal: If it is isosceles, then it has 2 equal sides.
3. Original statement: Only if f is integrable in an I interval, f is continuous in I.
Reciprocal: Only if f is continuous in I, f is integrable in an I interval.
4. Original statement: If an f function is derivable in a point, then it is continuous in that point.
Reciprocal: If an f function is continuous in a point, then it is derivable in that point.
5. Original statement: F is not an even function, to less that f(x) = f(-x).
Reciprocal: If f(x) = f(-x), then F is not an even function.
6. Original statement: If a < b, then a^2 < b^2.
Reciprocal: If a^2 < b^2, then a < b.
Now, to find the anti-reciprocal, you need to negate the statement of the reciprocal.
1. Anti-reciprocal of the original statement: A quadrilateral having 4 equal sides is not a sufficient condition for it to be a square.
2. Anti-reciprocal of the original statement: A triangle not having 2 equal sides is not a sufficient condition for it to be isosceles.
3. Anti-reciprocal of the original statement: Only if f is continuous in I, f is not necessarily integrable in an I interval.
4. Anti-reciprocal of the original statement: If an f function is continuous in a point, then it is not necessarily derivable in that point.
5. Anti-reciprocal of the original statement: If f(x) = f(-x), then F is not necessarily an even function.
6. Anti-reciprocal of the original statement: If a^2 < b^2, then a is not necessarily less than b.