Truth Tables Equivalent Statements

LOGIC

1. Indicate and justify which of the following sentences are statements.
a) She is mathematics major.
b) 128 = 26
c) x = 26
2. Write the statement bellow in symbolic form using the symbols ~, , and  and the indicated letters to represent component statements.
(m = "Juan is a math major", c = "Juan is a computer science major")
Juan is a math major but not a computer science major.
3. Let p be the statement "DATAENDFLAG is off," q the statement "ERROR equals 0," and r the statement "SUM is less than 1,000." Express the following sentences in symbolic notation.
a) DATAENDFLAG is off but ERROR is not equal to 0.
b) DATAENDFLAG is on and ERROR equals 0 but SUM is greater than or equal to 1,000.
4. Write a truth table for: (p  q)~(pq).

p q
T T
T F
F T
F F
5. Determine if the following statements are logically equivalent. Justify your answer using truth tables. Is ~(p q) equivalent to ~p  ~q?

p q
T T
T F
F T
F F
Final answer and explanation:
6. Use De Morgan's laws to negate:
Sam swims on Thursdays and Kate plays tennis on Saturdays.
7. Assume x is a particular real number and use De Morgan's laws to write a negation for
-4 < x < -1.
8. Construct a truth table for ~p q -> r

p Q R
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F

9. Use truth tables to verify that
a) p -> q  ~pq
p Q
T T
T F
F T
F F
The statements are/are not logically equivalent because ...
b) ~(p -> q)  p  ~q
P Q
T T
T F
F T
F F
The statements are/are not logically equivalent because...
10. Write negation for the following statement.
If today is Thanksgiving, then tomorrow is Friday.
11. Use a truth table to establish that: A conditional statement is not logically equivalent to its inverse.
p q
T T
T F
F T
F F
The statements are/are not logically equivalent because ...