Step-by-step explanation:
right from the start and based on the way the answer options are written, the 1., 4. and 5. answer options are correct.
but I am confused by the answer options. some indicate e.g. a converse or inverse statement to the original statement, but they are not.
let's review the definitions :
Statement If p , then q
Converse If q , then p
Inverse If not p , then not q
Contrapositive If not q , then not p
so, did your teacher mean "the contrapositive of ..." and "the converse of ..." ?
by adding the word "of" this would give everything a whole new meaning, and it would suddenly make sense.
under this assumption let's go through the 6 answer options in detail :
1.
the contrapositive of
"if AC does not equal BC, then C is not the midpoint of AB" is
"if C is the midpoint of AB, then AC equals BC".
that is the original statement and true.
so, 1. is correct.
2.
the converse of
"if AC equals BC, then C is the midpoint of AB" is
"if C is the midpoint of AB, then AC equals BC".
that is the original statement and true.
so, 2. is incorrect, as it says this should be false.
3.
the inverse of
"if AC equals BC, then C is the midpoint of AB" is
"if AC does not equal BC, then C is not the midpoint of AB".
that is true.
so, 3. is incorrect, as it says it should be false.
4.
the converse of
"if AC does not equal BC, then C is not the midpoint of AB" is
"if C is not the midpoint of AB, then AC does not equal BC".
that is true.
so, 4. is correct.
5.
the inverse of
"if AC does not equal BC, then C is not the midpoint of AB" is
"if AC equals BC, then C is the midpoint of AB".
that is true.
so, 5. is correct.
6.
the contrapositive of
"if AC equals BC, then C is the midpoint of AB" is
"if C is not the midpoint of AB, then AC does not equal BC".
that is true.
so, 6. is incorrect, as it says it should be false.
ok, this delivers in this case the same result, but it could be different with a different logic statement.
so, it is important to use the correct phrasing. please let your teacher know.
when there is a statement "abc", and then it says e.g.
the converse, "xyz", is false, that means that "xyz" is supposed to be already the converse of "abc".
but not that I have to create the converse OF "xyz" first.
for that you have to say
the converse of "xyz".
