** Contrapositive, Converse and
Inverse**

**Answers:**

1.If it's snowing, then the weather must be cold outside.

weather
, if it's snowing, then wis cold.w |
Formal logical format |

weather
, if ~(wis cold), then ~(it's snowing).w If it isn't cold outside, then it's not snowing. |
Contrapositive |

weather
, if wis cold, then it's snowing.w If it's cold outside, then it must be snowing. |
Converse |

weather
, if ~(it's snowing), then ~(wis cold).w If it isn't snowing, then it must not be cold outside. |
Inverse |

2. If an integer ** x** does not equal 1 or 0, then

xZ, if
1 or x
0, then x
> x^{2}x. |
Formal logical format |

xZ, if ~(
> x^{2}), then ~(x1
or x0)xor... xZ,
if x^{2}< , then x
= 1 or x = 0.x If x ^{2}< x for some integer
x, then x = 1 or x = 0 |
Contrapositive |

xZ, if
> x^{2}, then x1
or x0.xIf x > ^{2}x for some integer ,
then x is not equal to 1 or 0.x |
Converse |

xZ, if ~(1
or x0),
then ~(x > x^{2}).xIf an integer x equals 1 or 0, then x
is less than or equal to ^{2}x. |
Inverse |

3. If a student gets caught cheating, he/she will receive a grade of "F".

students ,
if s is caught cheating then s will receive
a grade of "F".s |
Formal logical format |

students ,
if ~(s will receive a grade of "F") then ~(s
is caught cheating).sor students ,
if s does not receive a grade of "F" then s
was not caught cheating.sIf a student did not receive a grade of "F", then
he/she was not caught cheating. |
Contrapositive |

students ,
if s receives a grade of "F" then s
was caught cheating.sIf a student receives a grade of "F", then he/she
was caught cheating. |
Converse |

students ,
if ~(s is caught cheating) then ~(s will receive
a grade of "F").sor students ,
if s is not caught cheating then s will not
receive a grade of "F".sIf a student is not caught cheating, then he/she will not
receive a grade of "F". |
Inverse |