Advertisements
Advertisements
Question
Prove that q → p ≡ ¬p → ¬q
Advertisements
Solution
| 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
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 ↔ q
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
Write the following sentences in symbolic form using statement variables p and q.
19 is not a prime number
Which one of the following sentences is a proposition?
4 + 7 = 12
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
Construct the truth table for the following statement.
¬P ∧ ¬q
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)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p → q) ∧ (q → r)) → (p → r)
Show that (p ∧ q) ≡ ¬p v ¬q
Show that ¬(p → q) ≡ p ∧¬q
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent
Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table
Choose the correct alternative:
Which one of the following statements has the truth value T?
Choose the correct alternative:
In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is
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
Choose the correct alternative:
The proposition p∧(¬p∨q)] is
