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Construct the truth table for the following statement pattern. (p ∧ r) → (p ∨ ~q) - Mathematics and Statistics

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प्रश्न

Construct the truth table for the following statement pattern.

(p ∧ r) → (p ∨ ~q)

बेरीज
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उत्तर

p q r ~q p∧r p∨~q (p∧r)→(p∨~q)
T T T F T T T
T T F F F T T
T F T T T T T
T F F T F T T
F T T F F F T
F T F F F F T
F F T T F T T
F F F T F T T
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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.11 | पृष्ठ ३३

संबंधित प्रश्‍न

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


Show that the following statement pattern is contingency.

(p → q) ↔ (~ p ∨ q)


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the dual statement of the following compound statement.

A number is a real number and the square of the number is non-negative.


Write the negation of the following statement.

All the stars are shining if it is night.


Construct the truth table for the following statement pattern.

(~p ∨ q) ∧ (~p ∧ ~q)


Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)


Using the truth table, prove the following logical equivalence.

[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


Write the converse, inverse, contrapositive of the following statement.

If a man is bachelor, then he is happy.


Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its


If p → (∼p v q) is false, then the truth values of p and q are respectively


The equivalent form of the statement ~(p → ~ q) is ______.


Which of the following is not true for any two statements p and q?


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p ∧ q) → (q ∨ p)


In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .

  1. `bar(PR)`  
  2. `bar(PM)`
  3. `bar(QM)`

Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.


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