My report in Computer Organization and Assembly Language

1. 
Report in Computer Organization
and Assembly Language
By: Raquel Mulles

2. 
 A truth table is a device used to determine when a
compound statement is true or false.
Truth Tables

3. 
Formal Name Symbol Read Symbolic Form
Negation ~ “Not” ~p
Conjunction ∧ “And” p ∧ q
Disjunction ∨ “Or” p ∨ q
Conditional → “If p then q” p → q
Biconditional ↔ “If and only
if”
p ↔ q
Connectives used in truth
tables

4. 

5. 
 Negation - represents the opposite of the statement
A True T statement becomes False F and a False F becomes
True T.
Negation

6. 
p ~p
T F
F T
Truth table for negation

7. 
 Let p represent the statement 4 > 1, q represent the
statement 12 < 9, and r represent 0 < 1. Decide
whether each statement is true or false.
 a) ~p ∧ ~q
 b) (~p ∧ r) ∨ (~q ∧ p)
Example: Mathematical
Statements

8. 
Solution
a) False, since ~ p is false.
b) True

9. 
 Conjunction - both statements must be true
Two True T statements will result in a True T
-Any other combination will produce a False F.
Conjunction

10. 
Truth table for conjunction
p q p ∧ q
T T T
T F F
F T F
F F F

11. 
 Let p represent the statement 4 > 1, q represent the
statement 12 < 9 find the truth of p ∧ q.
Solution
False, since q is false.
Example: Finding the Truth
Value of a Conjunction

12. 
 Disjunction - If either/or both statements are true,
the entire statement is true . One True T will result in
a True T statement; two False F statements will result in
a False F.
Disjunction

13. 
p q p ∨ q
T T T
T F T
F T T
F F F
Truth table for disjunction

14. 
 Let p represent the statement 4 > 1, q represent the
statement 12 < 9 find the truth of p ∨ q.
Solution
True, since p is true.
Example: Finding the Truth
Value of a Disjunction

15. 
Conditional
 Conditional - only false if the second statement is
false and it follows a true statement. All other
combinations of True T and False F are True T.

16. 
p q p → q
T T T
T F F
F T T
F F T
Truth table for conditional

17. 
Example of conditional
statement
Example:
 Given:
p: I do my homework
q: I get my allowance
 Problem:
What does p → q
represent?

18. 
 Solution
 In Example 1, p represents, "I do my homework,"
and q represents "I get my allowance." The
statement p q is a conditional statement which
represents "If p, then q."

19. 
 Biconditional - true only if both statements are true
or both statements are false. All other combination of
the True T and False F are False F.
Biconditional

20. 
p q p ↔ q
T T T
T F F
F T F
F F T
Truth table for
biconditional

21. 
Example:
 Given:
p: x + 2 = 7
q: x = 5
 Problem:
Write p ↔ q as a sentence. Then determine its truth
values p ↔ q.
Example of a biconditional
statement

22. 
 Solution
 The biconditonal p ↔ q represents the sentence:
"x + 2 = 7 if and only if x = 5." When x = 5, both p
and q are true. When x 5, both p and q are false.
A biconditional statement is defined to be true
whenever both parts have the same truth value.

23. 
Equivalent Expressions
 Equivalent expressions
are symbolic
expressions that have
identical truth values
for each corresponding
entry in a truth table.
 Hence ~(~p) ≡ p.
 The symbol ≡ means
equivalent to.

24. 
Negation of the
Conditional
 Here we look at the
negation of the
conditional.
 Note that the 4th and 6th
columns are identical.
 Hence p ^ ~q is
equivalent to ~(p  q).

25. 
 The negation of the conjunction p ^ q is given by ~(p
^ q) ≡ ~p v ~q.
“Not p and q” is equivalent to “not p or not q.”
 The negation of the disjunction p v q is given by ~(p v
q) ≡ ~p ^ ~q.
“Not p or q” is equivalent to “not p and not q.”
De Morgan’s Laws

26. 
 For any statements p and q,
~(p ∨ q) ≡ ~p ^ ~q and
~(p ^ q) ≡ ~p ∨ ~q

27. 
 Find a negation of each statement by applying De
Morgan’s Law.
a) I made an A or I made a B.
b) She won’t try and he will succeed.
 Solution
a) I didn’t make an A and I didn’t make a B.
b) She will try or he won’t succeed.
Example: Applying De
Morgan’s Laws

28. 
Watch and listen