Logic & Critical Thinking

Question 1

Equivalent quanitified statements

Answer 1

All A are B -> Some A are not B

Some A are B -> No A are B

Question 2

Conjunction

Answer 2

"p ^ q"
p and q
p but q
p yet q
p nevertheless q

Question 3

Disjunction

Answer 3

The compound statement formed by connecting statements with the word ‘or’
“p v q”

Question 4

Conditional Statement

Answer 4

The compound statement “If p, then q ”
is symbolized by p -> q

antecedent -> consequent

If p then q.
q if p.
p is sufficient for q.
q is necessary for p.
p only if q
only if q,p.

Question 5

Biconditional Statement

Answer 5

the compound statement
“p if and only if q” is symbolized by p q

p if and only if q
q if and only if p
If p then q, and if q then p.
p is necessary and sufficient for q.
q is necessary and sufficient for p.

Question 6

Dominance of connectives

Answer 6

Biconditional
Conditional
Conjunction/Disjunction
Negation

Question 7

Conjunction ^ (truth table)

Answer 7

Only true when both simple statements true (T T)

Question 8

Disjunction v (truth table)

Answer 8

False only when both components are false (F F).

Question 9

Conditional -> (truth table)

Answer 9

Only false when antecedent is true and consequent is false (T F)

Question 10

Biconditional (truth table)

Answer 10

True only when components have the same truth value (T T)(F F)

Question 11

Contrapositive of conditional

Answer 11

Both values negatted and switched. Equivalent to conditional statement

Question 12

Converse of conditional

Answer 12

Values switched. Not equivalent.

Question 13

Inverse of conditional

Answer 13

Negatting both values. Not Equivalent.

Question 14

Negation of conditional

Answer 14

~(p -> q) = p ^ ~q

Question 15

De Morgan’s Law

Answer 15

~(p ^ q) = ~p v ~q

~(p v q) = ~p ^ ~q

Question 16

Arguments

Answer 16

An argument consists of two parts: the given statements, called the premises, and a conclusion.

An argument is valid if the conclusion is true whenever the premises are assumed to be true.

Question 17

Fallacy

Answer 17

An argument that is not valid is said to be an invalid argument

Question 18

Tautology

Answer 18

All statements are true.

Question 19

TESTING THE VALIDITY OF AN ARGUMENT WITH A TRUTH TABLE

Answer 19

1. Use a letter to represent each simple statement in the argument.
2. Express the premises and the conclusion symbolically. (direct reasoning form)
3. Write a symbolic conditional statement of the form
   3 (premise 1) ^ (premise 2) ^ (premise n) -> conclusion,
   where n is the number of premises.
4. Construct a truth table for the conditional statement in step 3.
5. If the final column of the truth table has all trues, the conditional statement is a tautology and the argument is valid. If the final column does not have all trues, the conditional statement is not a tautology and the argument is invalid.

Question 20

Fallacy of the inverse (invalid argument)

Answer 20

p -> q
~p
_______
∴ ~q

Question 21

Contrapositive reasoning (valid argument)

Answer 21

p -> q
~q
_______
∴ ~p

Question 22

Disjunctive Reasoning (valid argument)

Answer 22

p v q
~q
_______
∴ p

p v q
~p
_______
∴ q

Question 23

Transitive Reasoning

Answer 23

p -> q
q -> r
\_\_\_\_\_\_\_
∴ p -> r
∴ ~r -> ~p