SOLUTION: Writing a converse and contra-positive of this statement? If a burglar lives in the house, then it is not safe to go outside tonight.

Question 478567: Writing a converse and contra-positive of this statement?
If a burglar lives in the house, then it is not safe to go outside tonight.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
statement = if a then b
converse = if b then a
inverse = if not a then not b
contra-positive = if not b then not a
the statement and its contra-positive are equivalent
this means that if the statement is true, then the contra-positive is true, and vice versa.
the converse and the inverse are equivalent.
this means that if the converse is true, then the inverse is also true, and vice versa.
if the statement is true, the converse may or may not be true.
your problem says to write a converse and a contra-positive statement.
we'll do that below:
statement:
if a burglar lives in the house, then it is not safe to go outside tonight.
converse:
if it is not safe to go outside tonight, then a burglar lives in the house.
contra-positive:
if it is safe to go outside tonight, then a burgles does not live in the house.
-----
let a = a burglar lives in the house.
let not a = a burglar does not live in the house.
let b = it is not safe to go outside tonight.
let not b = it is safe to go outside tonight.
statement translates to:
if a then b
converse translates to:
if b then a
contra-positive translates to:
if not b then not a
-----
this agrees with the rules stated above.

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