Discrete Mathematics Practical 9
Page 1 of 2 Oliver Hyde
Practical 9: Truth Tables
The aim of today’s practical is to create truth tables using Excel. An example of a truth table
for the logical AND function is shown in the following spreadsheet.
As always, p and q are propositions. Cell D3 contains the formula =AND(B3,C3).
Important Excel logical functions are:
Function Description
AND Returns TRUE if all of its arguments are TRUE
IF Specifies a logical test to perform
NOT Reverses the logic of its argument
OR Returns TRUE if any argument is TRUE
The IF function for specifying a logical test to perform should be familiar to you by now.
The AND, NOT and OR functions are the main focus of today’s practical.
Requirements
Open the spreadsheet Truth Tables.xlsx available on the Moodle page for this module and
complete all truth tables based on the following exercises.
Consider two propositions p and q. Complete the truth tables for the following logical
expressions:
❑ p OR q
❑ p XOR q
❑ p NAND q
❑ p NOR q
Discrete Mathematics Practical 9
Page 2 of 2 Oliver Hyde
XOR is the composition exclusive OR that yields true if exactly one (but not both) of two
conditions is true.
NAND is the composition NOT AND that yields true if any condition is false, and false if all
conditions are true.
NOR is equivalent to the composition NOT OR that yields false if any condition is true, and
true if all conditions are false.
Consider three propositions p, q and r. Complete the truth tables to verify the following rules
of logic:
❑ ~(p ʌ q) ≡ ~p v ~q
❑ ~(p v q) ≡ ~p ʌ ~q
❑ p v (q ʌ r) ≡ (p v q) ʌ (p v r)
❑ p ʌ (q v r) ≡ (p ʌ q) v (p ʌ r)
Submitting your Answers
❑ Save your Excel spreadsheet under the following name: the word Practical, followed
y a space and the practical number, i..e. Practical 9.
❑ Submit the spreadsheet via Moodle by Friday before 11:55 p.m. You may only submit
once. Late submissions are not permitted.
http:
mathworld.wolfram.com/ExactlyOne.html
http:
mathworld.wolfram.com/NOT.html
http:
mathworld.wolfram.com/AND.html
http:
mathworld.wolfram.com/True.html
http:
mathworld.wolfram.com/False.html
http:
mathworld.wolfram.com/False.html
http:
mathworld.wolfram.com/True.html
http:
mathworld.wolfram.com/NOT.html
http:
mathworld.wolfram.com/OR.html
http:
mathworld.wolfram.com/False.html
http:
mathworld.wolfram.com/True.html
http:
mathworld.wolfram.com/True.html
http:
mathworld.wolfram.com/False.html