Introductory Discrete Mathematics for Computer Science/Logic Review

[edit] Exercises

Resource type: this resource is a quiz.

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.