Advertisements
Advertisements
प्रश्न
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Advertisements
उत्तर
| p | q | p ↔ q | ¬(p ↔ q) | ¬q | p ↔ ¬q |
| T | T | T | T | F | F |
| T | F | F | F | T | T |
| F | T | T | F | T | T |
| F | F | F | T | F | F |
From the table, it is clear that
¬(p ↔ q) ≡ p ↔ ¬q
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
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 or all the angles of a triangle are not 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.
If 6 + 2 = 5, then the milk is white.
Which one of the following sentences is a proposition?
Peacock is our national bird
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
Construct the truth table for the following statement.
¬P ∧ ¬q
Construct the truth table for the following statement.
¬(P ∧ ¬q)
Construct the truth table for the following statement
(¬p → r) ∧ (p ↔ q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p → q) ↔ (¬p → q)
Show that (p ∧ q) ≡ ¬p v ¬q
Prove that q → p ≡ ¬p → ¬q
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:
| 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:
Which one of the following is not true?
