Logic Statements
Standard Form
Symbolic Representations
Truth Tables / Logical Equivalence
Implication/ Tautologies / Contradictions
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

Use letters and other symbols (~ , ∧,∨,→,↔,⟹,≡ ) to describe the following statements given:

p: John plays sports

q: Marc watches television.

John plays sports implies Marc watches television

p ⟹ q
100

Make the truth table for the following statement:

p → r

p → r
T
F
T
T
100

True or False: A statement that is not a tautology must be a contradiction.

False.
200
Is the following a logical statement?

A car is blue.

Yes.
200

p: My hair is brown.

q: My eyes are red.

Write the following in standard form:

(p ⟶ ~q)
If my hair is brown then my eyes are not red.
200

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 ∧ ~r) → r

(p ∧ ~r) → r
T
F
T
T
200

True or False: The negation of a tautology must be a contradiction.

True.
300
What type of statement is the following?

If a number is odd, then the number is divisible by 3.

Conditional.
300

p: My hair is brown.

q: My eyes are red.

Write the following in standard form:

~(~p → q)
My hair is not brown and my eyes are not red.
300

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:

(p ∧ ~q ) → r

(p ∧ ~q) → r
T
T
T
F
T
T
T
T
300

True or False: The conditional, if tautology then contradiction, is logically equivalent to the conjunction of a tautology and a contradiction.

True.
400
Is the following a statement?

The animal is a beagle implies the animal is a dog.

No.
400

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

p: John plays sports

q: Marc watches television.

If Marc watches television or John does not play sports, then Marc watches television.

(q ∨ ~p) → q
400

Are the following logically equivalent?

p ∧ (q ∨ r) and (p ∧ q) ∨ (p ∧ r)

Yes.
400

Is the following implication valid? Justify your answer (truth table).

[(p → q) ∧ ~q] ⟹ p ∨ q

No

(p → q) ∧ ~q] → p ∨ q
T
T
T
F
500
What type of elementary statement has the following truth table?
T
F
F
T
The biconditional.
500

p: My hair is brown.

q: My eyes are red.

Write the following in standard form:

~((p ⟶ ~q) ∨ q)
My hair is brown and my eyes are red, and my eyes are not red.
500

p: John plays sports

q: Marc watches television.

John does not play sports

~p
500

The conditional is logically equivalent to which of its variations?

Contrapositive
500

Is the following implication valid? Justify your answer (truth table).

p ∧ (q ∨ r) ⟹ (p ∧ q) ∨ (p ∧ r)

Yes

p ∧ (q ∨ r) → (p ∧ q) ∨ (p ∧ r)
T
T
T
T
T
T
T
T
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