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...

use the truth table excel sheet provided to complete this assignment


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 by 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