Hypothesis (p): A polygon is a square
Conclusion: (q): It is a rectangle
Inverse: q → p If a polygon is a rectangle, then it is a square
Converse: ~p → ~q If a polygon is not a square, then it is not a rectangle.
Contrapositive: ~q → ~p If a polygon is not a rectangle, then it is not a square
Your answers are correct
Answer:
Conditional statement: If a polygon is a square, then it is a rectangle.
hypothesis or p: If a polygon is a square,
conclusion or q: then it is a rectangle.
p-->q
In order to converse the conditional, switch the hypothesis and the conclusion. In other words q becomes p.
p: If a polygon is a rectangle,
q: then it is a square.
q-->p
In order to inverse the conditional, negate the hypothesis and negate the conclusion (of the original conditional statement) negate usually means opposite or 'not'
p: If a polygon is 'not' a square,
q: then it is 'not' a rectangle.
~p-->~q
symbol for 'not' is a sideways letter s which is called a tilde
Finally, in order to form the contrapositve, or create a new conditional from your original conditional, also known as, p-->q, you must interchange or switch the hypothesis and the conclusion, as well as negate, which means use the word 'not' or opposite, to both the hypothesis and the conclusion.
p: If a polygon is 'not' a rectangle,
q: then it is 'not' a square.
remember you're switching and negating
Looks like this:
~q-->~p
This all sounds wordy but a couple of examples and it gets much easier then it sounds at first.
A conditional statement is in the form "if p, then q" or p with an arrow q. (p-->q).
The converse of a conditional statement is in the form "if q, then p" or q-->p.
The inverse of a conditional statement is in the form "if not p, then not q" or ~p-->~q.
The contrapositive is in the form of "if not q, then not p" or ~q-->~p.
A conditional statement is not logically equivalent to its inverse or its converse. So just because the conditional statement is true does not mean that its inverse or converse is true. Parts of the conditional may be true or false independent of their relationship. So, do not assume p and q are true statements.
