Advertisements
Advertisements
Question
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p → q) ∧ (q → r)) → (p → r)
Advertisements
Solution
| p | q | r | p → q | q → r | p → r | (p → q) ∧ (q → r) | ((p → q) ∧ (q → r)) → (p → r) |
| T | T | T | T | T | T | T | T |
| T | T | F | T | F | F | F | T |
| T | F | T | F | T | T | F | T |
| T | F | F | F | T | F | F | T |
| F | T | T | T | T | T | T | T |
| F | T | F | T | F | T | F | T |
| F | F | T | T | T | T | T | T |
| F | F | F | T | T | T | T | T |
All the entries in the last column are only T.
∴ The given statement is a tautology.
APPEARS IN
RELATED QUESTIONS
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
¬ P
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
p ↔ q
Write the following sentences in symbolic form using statement variables p and q.
19 is not a prime number and all the angles of a triangle are equal
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number and all the angles of a triangle are equal
Determine the truth value of the following statement.
It is not true that 5 + 5 = 9 or Earth is a planet
Which one of the following sentences is a proposition?
3n ≤ 81, n ∈ N
Which one of the following sentences is a proposition?
Peacock is our national bird
Construct the truth table for the following statement.
¬P ∧ ¬q
Construct the truth table for the following statement.
(p v q) v ¬q
Show that p → q and q → p are not equivalent
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
Choose the correct alternative:
The operation * defined by a * b = `"ab"/7` is not a binary operation on
Choose the correct alternative:
Which one of the following statements has the truth value T?
Choose the correct alternative:
Which one of the following statements has truth value F?
Choose the correct alternative:
Which one is the contrapositive of the statement (p v q) → r?
Choose the correct alternative:
The proposition p∧(¬p∨q)] is
Choose the correct alternative:
Which one of the following is not true?
