Review of Logic Lesson
Back to ABE Math Tutorials/Logic
Exercises
Here are some exercises to practice your fluency with logical operators.
Problem 1
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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.
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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. |
