Logic

Question 1

is the study of methods of reasoning or argumentation. It is also a science or study of how to evaluate arguments and reasoning.

Answer 1

Logic

Question 2

is a declarative sentence which is true or false, but not both.

Answer 2

proposition or statement

Question 3

one and only one of which is assignable to any given statement is called the

Answer 3

‘truth value’ of that statement.

Question 4

are used to represent propositions, usually denoted by small letters, such as p, q, r, s and t.

Answer 4

Propositional variables

Question 5

contains one or more variables, that is, it is either true or false depending on the value of the placeholder.

Answer 5

open sentence

Question 6

on the other hand, is a mathematical sentence that is known to be either true or false.

Answer 6

closed sentence

Question 7

is a proposition formed from simple propositions using logical connectors or some combinations of logical connectors.

Answer 7

compound proposition

Question 8

are words, expressions, or phrases that point out the number of elements that a statement relates to

Answer 8

Quantifiers

Question 9

There are two types of quantifiers:

Answer 9

universal quantifier and existential quantifier.

Question 10

denoted by ∀, refers to the phrase “for all” or “for every” or “for each”. It asserts that the formula for any value of 𝑦 (the value as being taken from some given universe or the set of objects of interest).

Answer 10

universal quantifier

Question 11

denoted by ∃, refers to the phrase “there exists” or “for at least one” or “for some”. It asserts that the formula holds for at least one value of 𝑦.

Answer 11

existential quantifier

Question 12

Give any proposition “p”, its opposite is a statement “not p” referred to as the “negation” of the given proposition “p”. Likewise, “p” is the negation of “not p”.
Definition: If p is true, then ~p is false; and if p is false, then ~p is true.

Answer 12

Negation

Question 13

A compound statement formed by connecting two statements with the word “and” is called a ___. In symbols, it is written as “p ∧ q” which is read as “p and q”.
Definition: If p and q are true, then p ∧ q is true; otherwise p ∧ q is false.

Answer 13

Conjunctions

Question 14

A compound statement formed by connecting two statements with the word “or” is called ???. Symbolically, “p ∨ q” which is read as “p or q”.
Definition: If p and q are false, then p ∨ q is false; otherwise p ∨ q is true.

Answer 14

Disjunctions

Question 15

A compound statement formed by connecting two statements with the words “if…then” is called a ????. Symbolically, “p → q” which is read as “If p, then q” or “p implies q”.
The statement p is called antecedent and q is the consequent.

Answer 15

Conditional

Question 16

A compound statement formed by connecting two statements with the word “or” is called ???. Symbolically, “p ⨁ q” which is read as “p exclusive or q”.

Definition: Proposition is true when exactly one of its proposition is true and the other one is false.

Answer 16

exclusive or.

Question 17

A compound statement formed by connecting two statements with the words “if and only if” is called a ???. Symbolically, “p ↔ q” which read as “p if and only if q”.

Answer 17

Biconditional and Equivalent Statements

Question 18

The three important classes of compound statements namely ?,? and ?.

Answer 18

tautology, contradiction and contingency.

Question 19

A compound statement is a ? if its truth value is always T, regardless of the truth values of the statements of which it is composed.

Example:
The statement 𝑝→(𝑝∨𝑞) is a tautology.

Answer 19

tautology

Question 20

A compound statement is a ? if is truth value is always F, regardless of the truth values of its variables.

Example:
The statement (𝑝∧~𝑞)∧(𝑝∧𝑞) is a contradiction.

Answer 20

contradiction

Question 21

A compound statement is a ? if it is neither tautology nor contradiction.

Example:
The statement ((𝑝→𝑞)∧𝑞)→𝑝 is a contingency.

Answer 21

contingency

Question 22

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Answer 22

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