Logic and Formality

Question 1

Father of Logic

Answer 1

Aristotle

Question 2

An expression is completely formal when it is independent and precise.

Answer 2

True

Question 3

What is a STATEMENT?

Answer 3

main component of logic in mathematics.

Question 4

Propositional Variable

Answer 4

variable which used to represent a statement.

Question 5

Formal propositional

Answer 5

written using propositional logic notation, p, q, and r are used to represent
statements.

Question 6

used to combine simple statements which are referred to as compound statements.

Answer 6

Logical Connectives

Question 7

statement composed of two or more simple statements connected by logical
Connectives.

Answer 7

compound statement

Question 8

A statement which is not compound is said to be?

Answer 8

simple (also called atomic).

Question 9

NEGATION

Answer 9

The negation of the statement p is denoted by ~p, where ~ is the symbol for “not.”

Question 10

If p is true, ~p is false. Meaning, the truth value of the negation of a statement is always the reverse
of the truth value of the original statement.

Answer 10

True

Question 11

CONJUNCTION

Answer 11

CONJUNCTION

Question 12

If p is true and q is true, then p ∧ q is true; otherwise p ∧ q is false. Meaning, the conjunction of two
statements is true only if each statement is true.

Answer 12

True

Question 13

disjunction of the statement p, q is the compound statement “p or q.”

Answer 13

DISJUNCTION

Question 14

Symbolically, p ∨ q, where ∨ is the symbol for?

Answer 14

or

Question 15

If p is true or q is true or if both p and q are true, then p ∨ q is true; otherwise p ∨ q is false. Meaning, the disjunction of two statements is false only if each statement is false.

Answer 15

DISJUNCTION

Question 16

The conditional (or implication) of the statement p and q is the compound statement “if p then q.”

Answer 16

CONDITIONAL

Question 17

Symbolically, p → q, where → is the symbol for ?

Answer 17

“if then”

Question 18

In conditional, p is called hypothesis (or antecedent or
premise) and q is called conclusion (or consequent or consequence).

Answer 18

True

Question 19

The conditional statement p → q is false only when p is true and q is false; otherwise p → q is true.
Meaning p → q states that a true statement cannot imply a false statement.

Answer 19

True

Question 20

biconditional of the statement p and q is the compound statement “p if and only if q.”

Answer 20

BICONDITIONAL

Question 21

Symbolically, p ↔ q, where ↔ is the symbol for ?

Answer 21

“if and only if.”

Question 22

If p and q are true or both false, then p ↔ q is true; if p and q have opposite truth values, then p ↔ q is false.

Answer 22

BICONDITIONAL

Question 23

the statement p and q is the compound statement “p exclusive or q.”

Answer 23

EXCLUSIVE-OR

Question 24

Symbolically, p ⊕ q, where ⊕ is the symbol for ?

Answer 24

“exclusive or.”

Question 25

If p and q are true or both false, then p ⊕ q is false; if p and q have opposite truth values, then p ⊕ q
is true.

Answer 25

Exclusive-or