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x=y is the identity. It is its own inverse. So the inverse is y=x.
What isn't the inverse of this statement(?)
It is what you get in an inference, after negating both sides. That is, if you have a statement such as: if a then b the inverse of this statement is: if not a then not b Note that the inverse is NOT equivalent to the original statement.
Inverse
An Inverse statement is one that negates the hypothesis by nature. This will result into negation of the conclusion of the original statement.
x=y is the identity. It is its own inverse. So the inverse is y=x.
What isn't the inverse of this statement(?)
The inverse of a fraction is simple the result of flipping it's denominator with its numerator. It is equivalent to the statement (x/y)^-1 = y/x
It is what you get in an inference, after negating both sides. That is, if you have a statement such as: if a then b the inverse of this statement is: if not a then not b Note that the inverse is NOT equivalent to the original statement.
Answer this question… Which term best describes a proof in which you assume the opposite of what you want to prove?
f and g are both bijective mappings.
Inverse
"if a triangle is an equilateral triangle" is a conditional clause, it is not a statement. There cannot be an inverse statement.
Given a conditional statement of the form:If "hypothesis" then "conclusion",the inverse is:If "not hypothesis" then "not conclusion".
if A then B (original) if not A then not B (inverse)
The conditional statement "If A then B" is equivalent to "Not B or A" So, the inverse of "If A then B" is the inverse of "Not B or A" which is "Not not B and not A", that is "B and not A",
y -> x