Intermediate Logic: Lessons 6-9

NAME THOSE TERMS

100

A proposition that is always true due to its logical structure.

What is a TAUTOLOGY?

200

A proposition that is false by logical structure.

What is a SELF-CONTRADICTION?

300

Two propositions are ____________ if and only if they have identical truth values in a truth table.

What is LOGICALLY EQUIVALENT?

400

An argument is _______ when the premises imply the conclusion. In this type of argument, if the premises are true, then the conclusion must be true.

What is VALID?

500

True or False: The negation of any self-contradiction is a tautology.

What is TRUE?

TRUE, FALSE, OR *SHRUGS*

100

Assume A and B are true, X and Y are false, and P and Q are unknown. Determine the truth value of the following compound proposition:

~(A  X)

What is TRUE?

200

Assume A and B are true, X and Y are false, and P and Q are unknown. Determine the truth value of the following compound proposition:

(A  ~X)  ~B

What is FALSE?

300

Assume A and B are true, X and Y are false, and P and Q are unknown. Determine the truth value of the following compound proposition:

~P  (P  Y)

What is TRUE?

400

Assume A and B are true, X and Y are false, and P and Q are unknown. Determine the truth value of the following compound proposition:

(P v ~P)  ~B

What is FALSE?

500

Assume A and B are true, X and Y are false, and P and Q are unknown. Determine the truth value of the following compound proposition:

Q  (Y  Q)

What is UNKNOWN?

DON'T FORGET

100

The truth table for NEGATION.

What is:

_p__~p_

 T      F

 F      T

200

The truth table for CONJUNCTION.

What is:

__p__q____p  q_

T   T           T

T   F           F

F   T           F

F   F           F

300

The truth table for DISJUNCTION.

What is:

__p__q_____p v q_

 T    T            T

 T    F            T

 F    T            T

 F    F            F

400

The truth table for the CONDITIONAL.

What is:

_____p__q_____p  q__

 T     T           T

 T     F           F

 F     T           T

 F     F           T

500

Truth table for BICONDITIONAL.

What is:

____p__q____p  q__

 T    T          T

 T    F          F

 F    T          F

 F    F          T

EQUIVALENT OR CONTRADICTORY

100

Determine if this pair of propositions is logically equivalent, contradictory or neither.

p  ~q  ~p v q

What is CONTRADICTORY?

200

Determine if this pair of propositions is logically equivalent, contradictory or neither.

~p  q      p  ~q

What is LOGICALLY EQUIVALENT?

300

Determine if this pair of propositions is logically equivalent, contradictory or neither.

(p v q)    ~ (p  q)

What is NEITHER?

400

Determine if this pair of propositions is logically equivalent, contradictory or neither.

(~p  q)    (p v q)

What is LOGICALLY EQUIVALENT?

500

Determine if this pair of propositions is logically equivalent, contradictory or neither.

(p  q)     (p  ~q)

What is CONTRADICTORY?

SHORTCUTS

100

Use a shorter truth table to determine the validity of this symbolic argument.

p  ~q      p  r       ~(q  ~r)

What is INVALID?

200

Use a shorter truth table to determine the validity of this symbolic argument.

p  q      q  r      ~r       ~p

What is VALID?

300

Use a shorter truth table to determine the validity of this symbolic argument.

p  q      p v ~q       p  q

What is VALID?

400

Use a shorter truth table to determine the validity of this symbolic argument.

p v q      p  r      q  ~r       p  r

What is VALID?

500

Use a shorter truth table to determine the validity of this symbolic argument.

p  q     (q v r)  ~(q  r)     s  p     s      ~r

What is VALID?