Introductory Discrete Mathematics for Computer Science/Logic Review

Exercises

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

Problem 1

Template:ABCD Problem 2

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

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

$p$	$q$	$\mathrm{\neg }p$	$\mathrm{\neg }p\vee q$	$p\to q$
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. Template:ABCD