MSC_UNIT1_SECTIONA

The truth table of disjunction shows the results of the logical operation p ∨ q, where the output is true if at least one of the propositions p or q is true.

The implication proposition states that if proposition p is true, then proposition q is also true. For example, 'If I learn very hard, then I will get good marks in the exam.'

The conjunction is indicated by the symbol ∧ and is a proposition formed from two propositions, p and q, that is true only when both p and q are true.

Disjunction is a logical operation that combines two propositions p and q, resulting in true if at least one of the propositions is true, represented by p ∨ q.

A bi-conditional proposition, indicated by the symbol ↔, states that p if and only if q. It is true when both p and q are true or both are false.

When both p and q are true, the conjunction is true; when both are false, the conjunction is false.

A tautology is a proposition that is always true, regardless of the truth values of the propositional variables it contains.

A conditional proposition, also known as an implication, is a statement of the form 'if p then q', indicated by the symbol →, where p is the antecedent and q is the consequent.

The properties include that it is true when both propositions p and q are true or both are false, and false in all other cases.

The symbol ∧ represents the logical operation of conjunction.

A proposition that is always false is called a contradiction.

The properties of a conditional proposition state that it is true if p is false or both p and q are true, and it is false if p is true and q is false.

Today is Monday.

The truth table for bi-implication shows the truth values for p and q, indicating that p ↔ q is true when both are true or both are false, and false otherwise.

Disjunction is indicated by the symbol ∨ and is a proposition formed from two propositions, p and q, that is true when at least one of p or q is true.

A proposition is a declarative statement that can be classified as either true or false, but not both.

The bi-implication proposition p ↔ q signifies that I will get good marks if and only if I study hard.

A logical operation that results in true if at least one of the operands is true, represented by the symbol ∨.

4 + 4 = 8.

It is equal to the OR gate of digital electronics.

The disjunction is false only when both p and q are false; it is true when either p or q or both are true.

Negation is indicated by the symbol ∼ and represents the opposite truth value of a proposition; if a proposition p is true, then its negation ∼p is false, and vice versa.

The statement p ∨ p̄ represents that either the statement p is true, or the statement p̄ is true (that is, p is false), and this claim is always true.

A logical statement that expresses a relationship between two propositions, typically in the form 'If p, then q', represented by the symbol →.

If the number of primes is infinite, then Ooty is in Kerala.

It is equal to the EX-NOR gate of digital electronics.

The symbol ∨ represents the logical operation of disjunction.

The truth table for negation shows that if p is true (T), then ∼p is false (F), and if p is false (F), then ∼p is true (T).

The statement p ∧ p̄ claims that p is true, and at the same time, p̄ is also true (which means p is false), which is clearly impossible.

A logical statement that is true if both propositions are either true or false, expressed as 'p if and only if q', represented by the symbol ↔.

If Ooty is in Kerala, then the number of primes is infinite.

Some priority must be contained by each logical connective, and the order of this priority is important when solving questions.

Negation is equal to the NOT gate of digital electronics.

A compound statement that is always true regardless of the truth values of its components.

If the number of primes is not infinite, then Ooty is not in Kerala.

Connectives are logical operators that connect propositions, including negation, conjunction, and disjunction.

They contain the commutative and associative properties.

Conjunction is equal to the AND gate of digital electronics.

A declarative statement that can be classified as either true or false.

If Ooty is not in Kerala, then the number of primes is not infinite.

A tautology is a statement that is always true regardless of the truth values of its components.

Implication or conditional do not contain commutative or associative properties.

The negation of proposition p, meaning 'It is not cold' if p is 'It is cold'.

A contradiction is a statement that is always false, regardless of the truth values of its components.

The symbol for Negation is ⌉ or ∼ or ' or - .

The conjunction of propositions p and q, meaning 'It is cold and raining'.

The symbol for Conjunction is ∧.

The disjunction of propositions p and q, meaning 'It is cold or raining'.

The disjunction of proposition q and the negation of proposition p, meaning 'It is raining or it is not cold'.