Advertisements
Advertisements
प्रश्न
Prove that q → p ≡ ¬p → ¬q
Advertisements
उत्तर
| p | q | q → p | ¬p | ¬q | ¬p → ¬q |
| T | T | T | F | F | T |
| T | F | T | F | T | T |
| F | T | F | T | F | F |
| F | F | T | T | T | T |
The entries in the columns corresponding to q → p and ¬p → ¬q are identical and hence they are equivalent.
∴ q → q = ¬p → ¬q
Hence proved.
APPEARS IN
संबंधित प्रश्न
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
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 v q
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
Determine the truth value of the following statement.
If 6 + 2 = 5, then the milk is white.
Determine the truth value of the following statement.
11 is a prime number and all the sides of a rectangle are equal
Which one of the following sentences is a proposition?
4 + 7 = 12
Which one of the following sentences is a proposition?
How tall this mountain is!
Write the converse, inverse, and contrapositive of the following implication.
If x and y are numbers such that x = y, then x2 = y2
Write the converse, inverse, and contrapositive of the following implication.
If a quadrilateral is a square then it is a rectangle
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p ∧ q) ∧¬ (p v q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p → q) ↔ (¬p → q)
Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent
Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table
Choose the correct alternative:
Which one of the following statements has truth value F?
Choose the correct alternative:
If a compound statement involves 3 simple statements, then the number of rows in the truth table is
Choose the correct alternative:
Which one is the contrapositive of the statement (p v q) → r?
Choose the correct alternative:
The truth table for (p ∧ q) v ¬q is given below
| p | q | (p ∧ q) v ¬q |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is true?
Choose the correct alternative:
Which one of the following is incorrect? For any two propositions p and q, we have
Choose the correct alternative:
| p | q | (p ∧ q) → ¬p |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is correct for the truth value of (p ∧ q) → ¬p
