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Show that ¬(p ↔ q) ≡ p ↔ ¬q - Mathematics

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प्रश्न

Show that ¬(p ↔ q) ≡ p ↔ ¬q

तक्ता
बेरीज
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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

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Mathematical Logic
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पाठ 12: Discrete Mathematics - Exercise 12.2 [पृष्ठ २४९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 12 Discrete Mathematics
Exercise 12.2 | Q 11 | पृष्ठ २४९

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


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.


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?

What are you doing?


Which one of the following sentences is a proposition?

3n ≤ 81, n ∈ N


Construct the truth table for the following statement.

¬P ∧ ¬q


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)


Show that (p ∧ q) ≡ ¬p v ¬q


Prove that q → p ≡ ¬p → ¬q


Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent


Choose the correct alternative:

Which one of the following statements has the truth value T?


Choose the correct alternative:

Which one is the inverse of the statement (p v q) → (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:

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


Choose the correct alternative:

The dual of ¬(p v q) v [p v(p ∧ ¬r)] is


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