p.1
Propositions and Truth Values
What is a proposition in mathematical logic?
A declarative statement that can be either true or false, but not both.
What is the truth table for a proposition p and its negation ∼p?
p: T, ∼p: F; p: F, ∼p: T.
p.5
Bi-conditional Statements
What does the bi-implication proposition p ↔ q signify?
I will get good marks if and only if I study hard.
p.5
Tautology and Contradiction
What is a contradiction?
A proposition that is always false.
p.7
Propositions and Truth Values
Which statement is a proposition from the options given?
The only odd prime number is 2.
Provide an example of conjunction using propositions p and q.
If p: I am a good student and q: I like my math teacher, then p ∧ q: I am a good student and I like my math teacher.
p.5
Tautology and Contradiction
What is a tautology?
A proposition that is always true, regardless of the truth values of its variables.
p.8
Conditional Statements
What is the contrapositive statement for p: 'The number of primes is infinite' and q: 'Ooty is in Kerala'?
¬q → ¬p: 'If Ooty is not in Kerala, then the number of primes is not infinite.'
What does the truth table for conjunction look like?
T T T, T F F, F T F, F F F.
p.1
Propositions and Truth Values
What is propositional logic?
A branch of logic that deals with propositions and their connectivity.
Provide an example of a proposition and its negation.
If p: I am a good student, then ∼p: I am not a good student.
p.3
Conditional Statements
When is a conditional proposition false?
When p is true and q is false.
p.4
Bi-conditional Statements
When is a bi-conditional proposition true?
When both p and q are true, or both are false.
p.4
Bi-conditional Statements
What is a bi-conditional proposition?
A proposition that has the form 'p if and only if q'.
p.4
Bi-conditional Statements
What does the truth table for bi-implication show?
The truth values of p ↔ q based on the truth values of p and q.
p.3
Conditional Statements
When is a conditional proposition true?
When p is false or both p and q are true.
What are the main topics covered in Unit 1 of Mathematical Logic?
Statements, Connectives, Negation, Conjunction, Disjunction, Truth Tables, Conditional and Bi-conditional Statements, Tautology, and Contradiction.
p.4
Conditional Statements
What does the implication proposition p → q represent?
If I learn very hard, then I will get good marks in the exam.
p.8
Conditional Statements
What is the inverse statement for p: 'The number of primes is infinite' and q: 'Ooty is in Kerala'?
¬p → ¬q: 'If the number of primes is not infinite, then Ooty is not in Kerala.'
p.6
Logical Connectives and Their Properties
Which logical connectives contain commutative and associative properties?
Negation, disjunction, conjunction, and bi-conditional.
p.8
Conditional Statements
What are the component statements p and q for the conditional statement p → q: 'If today is Monday, then 4 + 4 = 8'?
p: Today is Monday; q: 4 + 4 = 8.
p.8
Conditional Statements
What is the conditional statement for p: 'The number of primes is infinite' and q: 'Ooty is in Kerala'?
p → q: 'If the number of primes is infinite, then Ooty is in Kerala.'
p.5
Tautology and Contradiction
What does the expression p ∨ p̄ represent?
It states that either p is true or p̄ is true, which is always true.
p.6
Logical Connectives and Their Properties
Which logical connectives do not contain commutative or associative properties?
Implication and conditional.
p.1
Set Theory and Venn Diagrams
What are the laws of set theory?
They include operations on sets and the relationships between sets and subsets.
p.8
Conditional Statements
What is the converse statement for p: 'The number of primes is infinite' and q: 'Ooty is in Kerala'?
q → p: 'If Ooty is in Kerala, then the number of primes is infinite.'
p.4
Bi-conditional Statements
When is a bi-conditional proposition false?
In all other cases where p and q do not match.
What does q ∨ ¬p represent when p is 'It is cold' and q is 'It is raining'?
It is raining or it is not cold.
What happens to the truth value of a proposition when it is negated?
If the proposition is true, the negation is false; if the proposition is false, the negation is true.
p.5
Tautology and Contradiction
What does the expression p ∧ p̄ represent?
It claims that p is true and p̄ is also true, which is impossible, hence false.
p.6
Logical Connectives and Their Properties
Why is the priority of logical connectives important?
It affects the order of operations when solving logical expressions.
When is the disjunction p ∨ q true?
When either p or q or both are true.
p.8
Conditional Statements
What is the truth value of p → q when q is true?
The truth value is T (true).
