Introductory Discrete Mathematics for Computer Science/Logic Review

Exercises

Type classification: this is a quiz resource.

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

Problem 1

Write statements using logical operators and different letters for the following conditions:

It is not cold. This is the statement: $\urcorner c$.

It is cold and also the water is running. This is the statement: $c\wedge w$.

I am either wearing shorts or pants, but not both. This is the statement: $s\oplus p$.

There is food, water or both. This is the statement: $f\vee w$.

Problem 2

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

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

$p\,\!$	$q\,\!$	$\neg p$	$\neg p\vee q$	$p\to q$
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.

Which two statements are logically equivalent?

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.