Logic Statements
Standard and Symbolic Form
Truth Tables / Logical Equivalence
100
Is the following a logical statement?
Go Mavs!
No.
100
p: My hair is brown.
q: My eyes are red.
Write the following in standard form:
p ∧ q
My hair is brown and my eyes are red.
100
Make the truth table for the following statement:
p → q
| p → q |
| T |
| F |
| T |
| T |
200
Is the following a logical statement?
A car is blue.
Yes.
200
Write in symbolic form
p: John plays sports
q: Marc watches television.
John does not play sports or Marc watches television
~p ∨ q
200
Make the truth table for the following statement:
(p ∧ ~q) → q
| (p ∧ q) → q |
| T |
| F |
| T |
| T |
300
What type of statement is the following?
If a number is odd, then the number is divisible by 3.
Conditional.
300
Write symbolically
p: John plays sports
q: Marc watches television.
John plays sports if and only if Marc does not watch television
p ⟷ ~q
300
Make the truth table for the following statement:
Tautology
400
What type of statement is the following?
The animal is a cat or the animal is a dog.
Disjunction
400
Write in words as a conjunction
p: My hair is brown.
q: My eyes are red.
Write the following in standard form:
~(q ∨ ~p)
My eyes are not red and my hair is brown.
400
Write the Converse, Inverse, and Contrapositive for
If I study, then I pass the test.
Converse: If I pass the test, then I study
Inverse: If I do not study, then I do not pass the test
Contrapositive: If I do not pass the test, then I do not study.
500
Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.")
a. Some math tests are not fun.
b. None of the students failed the test.
a. All math tests are fun.
b. Some of the students failed the test.
500
Write the statement in words
p: John plays sports
q: Marc watches television.
(q ∨ ~p) → q
If Marc watches television or John does not play sports, then Marc watches television.
500
Write the conclusion or not valid
If Jake studied, then he passed the test.
If he passed the test, then he was happy
If Jake studied, then he was happy