# Review of Logic Lesson

Back to ABE Math Tutorials/Logic

## Exercises

Here are some exercises to practice your fluency with logical operators.

**Problem 1**

It is not cold. This is the statement: [math]\urcorner c[/math]. |
It is cold and also the water is running.This is the statement: [math]c \wedge w [/math]. |
I am either wearing shorts or pants, but not both.This is the statement: [math]s \oplus p [/math]. |
There is food, water or both.This is the statement: [math]f \vee w [/math]. |

**Problem 2**

Draw the relevant truth tables, to show that [math]\neg p \vee q[/math] is or is not logically equivalent to [math]p \to q[/math].

ANSWER: These statements are logically equivalent. Here is the truth table for both:

[math]p \,\![/math] | [math]q \,\![/math] | [math]\neg p[/math] | [math]\neg p \vee q[/math] | [math]p \to q[/math] |
---|---|---|---|---|

T | T | F | T | T |

T | F | F | F | F |

F | T | T | T | T |

F | F | T | T | T |

**Problem 3**

Show that a conditional statement is logically equivalent to its contrapositive.

**Problem 4**

This problem also requires you to draw the relevant truth tables.

The converse of a conditional statement and the statement itself. WRONG! Try again. |
The converse and inverse of a conditional statement.Correct! |
A conditional statement and its inverse.WRONG! Try again. |
The converse and contrapositive of a conditional statement.WRONG! Try again. |